%CabrelliHeilMolter98 % LLS Lai-Schumaker book \rhl{CabHM98} \refJ Cabrelli, C., Heil, C., Molter, U.; Accuracy of lattice translates of several multidimensional refinable functions; \JAT; 95; 1998; 5--52; %Cadwell61 \rhl{C} \refJ Cadwell, J. H.; A Least squares surface-fitting program; \C; 3; 1961; 266--269; % should be 4; 1969;??? %CadwellWilliams61 \rhl{C} \refJ Cadwell, J. H., Williams, D. E.; Some orthogonal methods of curve and surface fitting; \C; 4; 1961; 260--264; % should be 1969;??? %CaiMehlum97 % author 03dec99 \rhl{C} \refJ Cai, Xing, Mehlum, Even; Application of Cauchy integrals and singular integral equations in scattered data problems; \BIT; xx; xxx; xxx--xxx; % constructing `smooth' surfaces with desired discontinuities through given data %Cain71 \rhl{C} \refR Cain, J. M; A study of multiquadric equations; Rpt.\ 1-11, U.S. Army Topographic Command; 1971; %CallJudd74 % sonya \rhl{C} \refJ Call, E. S., Judd, F. F.; Surface fitting by separation; \JAT; 12; 1974; 283--290; %Calladine86 % carl \rhl{C} \refP Calladine, C. R.; Gaussian curvature and shell structures; \SurfacesI; 179--196; %CalvettiReicher92 % carl \rhl{C} \refJ Calvetti, D., Reichel, L.; A Chebyshev-Vandermonde solver; \LAA; 172; 1992; 219--230; %Calvi93 % shayne 6aug96 \rhl{C} \refJ Calvi, J. P.; A convergence problem for Kergin interpolation; Proc.\ Edin.\ Math.\ Soc.; 37; 1994; 175--183; %Calvi93 % shayne 6aug96 \rhl{C} \refJ Calvi, J. P.; Interpolation with prescribed analytic functionals; \JAT; 75(2); 1993; 136--156; % related to Kergin interpolation %Calvi93 % shayne 6aug96 \rhl{C} \refJ Calvi, J. P.; Interpolation in Fr\'echet spaces with an application to complex function theory; Indag.\ Math.; 4(1); 1993; 17--26; % related to Kergin interpolation %Candes00 % larry 20apr00 \rhl{} \refP Cand\`es, Emmanuel J.; Ridgelets and their derivatives: representation of images with edges; \Stmalof; 95-104; %CandesDonoho00 % larry 20apr00 \rhl{} \refP Cand\`es, Emmanuel J., Donoho, David L.; Curvelets: a surprisingly effective nonadaptive representation for objects with edges; \Stmalof; 105--120; %Canonne94 % larry \rhl{C} \refP Canonne, J. C.; A necessary and sufficent condition for the $C^k$ continuity of triangular rational surfaces; \ChamonixIIa; 75--82; %Cantoni71 % larry \rhl{C} \refJ Cantoni, A.; Optimal curve fitting with piecewise linear functions; IEEE Trans.\ Computers ; C-20; 1971; 59--67; %Cantoni71b \rhl{C} \refJ Cantoni, A.; Improving transient response calculations; Austral.\ Comp.\ J.; 3; 1971; 156--160; %Cantoni72 \rhl{C} \refJ Cantoni, A.; Curve fitting with piecewise linear functions; Proc.\ I. R. E. E, Australia ; 33; 1972; 417--423; %CaoGonska89 %larry \rhl{C} \refJ Cao, J.-D., Gonska, H. H.; Approximation by Boolean sums of positive linear operators III: Estimates for some numerical approximation schemes; \NFAO; 10; 1989; 643--672; %CaoGonskaKacso97 % larry 10sep99 \rhl{CGK} \refP Cao, J., Gonska, H. H., Kacs\'o, D. P.; On some polynomial curves derived from trigonometric kernels; \ChamonixIIIa; 53--60; %CaoHua91a % greg \rhl{C} \refJ Cao, Y., Hua, X.; The convexity of quadratic parametric triangular Bernstein-B\'ezier surfaces; \CAGD; 8; 1991; 1--6; %CaramanlianSelbyHill78 \rhl{C} \refJ Caramanlian, C., Selby, K. A., Hill, G. T.; A quintic conforming plate bending triangle; Internat.\ J.\ Numer.\ Meth.\ Engr.; 12; 1978; 1109--1130; %Carasso66 \rhl{C} \refD Carasso, C.; M\'ethodes num\'eriques pour l'obtention de fonctions-spline; Univ.\ of Grenoble; 1966; %Carasso67 % larry \rhl{C} \refJ Carasso, C.; M\'ethode generale de construction de fonctions-spline; Rev.\ Francaise Informat Recherche Oper.; 1; 1967; 119--127; %Carasso67a \rhl{C} \refQ Carasso, C.; M\'ethodes num\'eriques de fonctions-spline; (5eme Congres de L'Alfiro, Lille), xxx (ed.), xxx (xxx); 1967; 506--509; %Carasso67b \rhl{C} \refQ Carasso, C.; Obtention de la derivee d'une fonction donnee par points; (Procedures Algol en Analyse Num.\ 1), xxx (ed.), Centre National de la Recherche Scientifique (Paris); 1967; 300--301; %Carasso67c \rhl{C} \refQ Carasso, C.; Obtention d'une fonction-spline d'interpolation d'ordre $k$ par une methode d'integration locale; (Procedures Algol en Analyse Num.\ 1), xxx (ed.), Centre National de la Recherche Scientifique (Paris); 1967; 288--291; %Carasso67d \rhl{C} \refQ Carasso, C.; Obtention d'une fonction lisse passant par des points donnees et ayant en ces points des derivees donnees fonction-spline d'Hermite; (Procedures Algol en Analyse Num.\ 1), xxx (ed.), Centre National de la Recherche Scientifique (Paris); 1967; 295--299; %Carasso67e \rhl{C} \refQ Carasso, C.; Methode pour l'obtention de fonction-spline d'interpolation d'ordre deux; (Procedures Algol en Analyse Num.\ 1), xxx (ed.), Centre National de la Recherche Scientifique (Paris); 1967; 292--294; %CarassoLaurent68 \rhl{C} \refQ Carasso, C., Laurent, P. J.; On the numerical construction and the practical use of interpolating Spline Functions; (Info.\ Processing 68, Vol.\ l), xxx (ed.), North Holland (Amsterdam); 1969; 86--89; %CarassoLaurent78 % Laurent P. J. 20jan03 \rhl{} \refJ Carasso, C., Laurent, P. J.; Un algorithme de minimisation en chaine en optimisation convexe; \SJCO; 16; 1978; 209--235; %CarlbomChakravartyVandersschel85a % carl \rhl{C} \refJ Carlbom, Ingrid, Chakravarty, Indranil, Vandersschel, David A.; A hierarchical data structure for representing the spatial decomposition of 3-D objects; \ICGA; 5(4); 1985; 24--31; %Carlson99 \rhl{C} \refR Carlson, R. E.; Shape preserving interpolation; LLNL, 97--113; xx; %CarlsonBC91 % carl \rhl{C} \refJ Carlson, B. C.; B-splines, hypergeometric functions, and Dirichlet averages; \JAT; 67; 1991; 311--325; %CarlsonBC91 % carl \rhl{C} \refJ Carlson, B.C.; B-splines, hypergeometric functions, and Dirichlet averages; \JAT; 67; 1991; 311--325; %CarlsonFoley90 \rhl{C} \refR Carlson, R. E., Foley, T. A.; The parameter $R^2$ in multiquadric interpolation; Lawrence Livermore National Laboratory, Preprint UCRL-JC-104724; 1990; %CarlsonFoley91a \rhl{C} \refJ Carlson, R. E., Foley, T. A.; The parameter $r^2$ in multiquadric interpolation; \CMA; 21; 1991; 29--42; %CarlsonR70 \rhl{C} \refR Carlson, R. E.; Some remarks on bicubic splines; Livermore; 1970; %CarlsonR71 % sonya \rhl{C} \refR Carlson, R. E; On piecewise polynomial interpolation in rectangular polygons; xxx; 1971; %CarlsonR82 \rhl{C} \refJ Carlson, R. E.; A bivariate interpolation algorithm for scattered data; \RMJM; xx; xx; xx; %CarlsonRFritsch82 \rhl{C} \refR Carlson, R. E., Fritsch, F. N.; Piecewise cubic Hermite interpolation package; Livermore; 1982; %CarlsonRFritsch85 % larry \rhl{C} \refJ Carlson, R. E., Fritsch, F. N.; Monotone piecewise bicubic interpolation; \SJNA; 22; 1985; 386--400; %CarlsonRFritsch89 % larry \rhl{C} \refJ Carlson, R. E., Fritsch, F. N.; An algorithm for monotone piecewise bicubic interpolation; \SJNA; 26; 1989; 230--238; %CarlsonRFritsch91 % larry \rhl{C} \refJ Carlson, R. E., Fritsch, F. N.; A bivariate interpolation algorithm for data which are monotone in one variable; \SJSSC; 12; 1991; 859--866; %CarlsonRHall69 \rhl{C} \refR Carlson, R. E., Hall, C. A.; On the nonlocalness of spline-interpolation; WAPD-T-2244; 1969; %CarlsonRHall70 \rhl{C} \refR Carlson, R. E., Hall, C. A.; Spline extrapolation and $L$-shaped regions; Livermore; 1970; %CarlsonRHall71 % sonya \rhl{C} \refJ Carlson, R. E., Hall, C. A.; On piecewise polynomial interpolation in rectangular polygons; \JAT; 4; 1971; 37--53; %CarlsonRHall72 % sonya \rhl{C} \refJ Carlson, R. E., Hall, C. A.; Bicubic spline interpolation in rectangular polygons; \JAT; 6; 1972; 366--377; %CarlsonRHall73 % sonya \rhl{C} \refJ Carlson, R. E., Hall, C. A.; Error bounds for bicubic spline interpolation; \JAT; 7; 1973; 41--47; %CarlsonRHall73b % sonya \rhl{C} \refJ Carlson, R. E., Hall, C. A.; Bicubic spline interpolation in $L$-shaped domains; \JAT; 8; 1973; 62--68; %CarlsonRHall99 \rhl{C} \refR Carlson, R. E., Hall, C. A.; Bicubic spline interpolation and approximation in right triangles; xx; 19xx; %Carnicer91 \rhl{C} \refJ Carnicer, J. M.; % . sherm, update page numbers On best constrained interpolation; \NA; 1; 1991; 155--176; %Carnicer95 % LLS Lai-Schumaker book \rhl{Car95} \refJ Carnicer, J. M.; Multivariate convexity preserving interpolation by smooth functions; \AiCM; 3; 1995; 395--404; %CarnicerBastero94a % carl \rhl{C} \refJ Carnicer, J. M., Bastero, J.; On best interpolation in Orlicz spaces; \JATA; 10(4); 1994; 72--84; %CarnicerDahmen92 %ming Lai-Schumaker book \rhl{CarD92} \refJ Carnicer, J. M., Dahmen, W.; Convexity preserving interpolation and Powell--Sabin elements; \CAGD; 9; 1992; 279--289; %CarnicerDahmen94 % LLS Lai-Schumaker book \rhl{CarD94} \refJ Carnicer, J. M., Dahmen, W.; Characterization of local strict convexity preserving interpolation methods by $C\sp 1$ functions; \JAT; 77; 1994; 2--30; %CarnicerFloaterPena97 % LLS Lai-Schumaker book \rhl{CarFP97} \refJ Carnicer, J. M., Floater, M. S., Pe\~na, J. M.; Linear convexity conditions for rectangular and triangular Bernstein--B\'ezier surfaces; \CAGD; 15; 1997; 27--38; %CarnicerGasca00 % author 03apr06 \rhl{} \refP Carnicer, J. M., Gasca, M.; Planar configurations with simple Lagrange formula; \OsloII; 55--62; %CarnicerGasca01a % sauer \refJ Carnicer, J. M., Gasca, M.; A conjecture on multivariate polynomial interpolation; Revista Academia de Ciencias de Madrid, Serie A Matem.; 95(1); 2001; 145--154; % http://pcmap.unizar.es/~gasca/investig/conjecture.pdf % detailed proofs of the GM conjecture (in the bivariate case) for $n\le 4$ % as an alternative to Busch90. %CarnicerGasca03 % carl 20nov03 \rhl{C} \refP Carnicer, J. M., Gasca, M.; On Chung and Yao's geometric characterization for bivariate polynomial interpolation; \Stmalodtw; 21--30; % introduces the CG conjecture: every (planar) GCn-set has at least 3 lines % containing n+1 of the points, then proves that if the GM conjecture holds % for all n le some N, the CG conjecture also holds for all such n. %CarnicerGasca04a % sauer \rhl{} \refJ Carnicer, J., Gasca., M.; Classification of bivariate GC configurations for interpolation; \AiCM; 20; 2004; 5--16; %CarnicerGasca05 % author 03apr06 \rhl{} \refJ Carnicer, J. M., Gasca, M.; Generation of lattices of points for bivariate interpolation; \NA; 39(1-3); 2005; 69--79; %CarnicerGasca0x % sauer \rhl{} \refJ Carnicer, J., Gasca., M.; Interpolation lattices generated by cubic pencils; \AiCM; xx; 200x; xxx--xxx; %CarnicerGasca89a % . 14may99 \rhl{C} \refP Carnicer, J. M., Gasca, M.; On finite element interpolation problems; \Oslo; 105--113; %CarnicerGasca89b % . 14may99 \rhl{C} \refP Carnicer, J. M., Gasca, M.; On the evaluation of multivariate Lagrange formulae; \MvatIV; 65--72; %CarnicerGasca90 % larry, carl \rhl{C} \refJ Carnicer, J., Gasca, M.; Evaluation of multivariate polynomials and their derivatives; \MC; 54(189); 1990; 231--243; %CarnicerGascaSauer06 % author 03apr06 \rhl{} \refJ Carnicer, J. M., Gasca, M., Sauer, T.; Interpolation lattices in several variables; % ms; 2004; \NM; 102; 2006; 559--581; % extension of GascaSauer00 %CarnicerGodes0x % author \rhl{CGo} \refJ Carnicer, J. M., God\'es, C.; Geometric characterization and generalized principal lattices; % to appear in \JAT; 2005; \JAT; 143(1); 2006; 4--14; %CarnicerGoodmanPena94 \rhl{C} \refR Carnicer, J. M., Goodman, T. N. T., Pena, J. M.; A generalization of the variation diminishing property; xx; 1994; %CarnicerMainar00 % larry 20apr00 \rhl{} \refP Carnicer, J. M., Mainar, E.; Factorizations of normalized totally positive systems; \Stmalod; 1--8; %CarnicerMicchelliPena93 % carlrefs 20nov03 \rhl{} \refJ Carnicer, J. M., Micchelli, C. A., Pen\~na, J. M.; Almost strictly totally positive matrices; \NA; 2(2); 1992; 225--236; %CarnicerPena93a % carlrefs 20nov03 \rhl{} \refJ Carnicer, J. M., Pe\~na, J. M.; Shape preserving representations and optimality of the Bernstein basis; \AiCM; 1; 1993; 173--196; %CarnicerPena93b % carl 20nov03 \rhl{CP} \refJ Carnicer, J. M., Pe\~na, J. M.; A Marsden's type identity for periodic trigonometric splines; \JAT; 75(3); 1993; 248--265; %CarnicerPena94a % larry \rhl{C} \refP Carnicer, J. M., Pe\~na, J. M.; Monotonicity preserving representations; \ChamonixIIa; 83--90; %CarnicerPena94b % authors 02feb01 \rhl{C} \refJ Carnicer, J. M., Pe\~na, J. M.; Totally positive bases for shape preserving curve design and optimality of B-splines; \CAGD; 11; 1994; 635--656; %CarnicerPena94c % LLS Lai-Schumaker book \rhl{CarP94} \refJ Carnicer, J. M., Pe\~na, J. M.; Least supported bases and local linear independence; \NM; 67; 1994; 289--301; %CarrollBraess74 % sonya \rhl{C} \refJ Carroll, M. P., Braess, D.; On uniqueness of $L_1$ approximation for certain families of spline functions; \JAT; 12; 1974; 362--364; %CarstensenMuhlbackSchmidt94 \rhl{C} \refR Carstensen, C., M\"uhlback, G., Schmidt, G.; DeCasteljau's algorithm is an extrapolation method; CAGD; 1994; %Cartwright99 % carl 20apr00 \rhl{C} \refB Cartwright, David E.; Tides: a Scientific History; Cambridge University Press (Cambridge, UK); 1999; % nice examples of practical harmonic analysis %Carusnikov69 % larry \rhl{C} \refJ Carusnikov, V. D.; On the problem of optimization of algorithms for approximate integration of functions of several variables; Soviet Math.\ Dokl.; 10; 1969; 1355--1359; %CasaleBobrow89a % greg \rhl{C} \refJ Casale, M. S., Bobrow, J. E.; A set operation algorithm for sculptured solids modeled with trimmed patches; \CAGD; 6; 1989; 235--247; %CasazzaFickusKovacevicLeonTremain03 % shayne 23jun03 \rhl{} \refR Casazza, P. G., Fickus, M. C., Kova\v cevi\' c, J., Leon, M. T., Tremain, J. C.; A physical interpretation for finite tight frames; preprint; 2003; %CasazzaHanLarson99a % shayne \rhl{} \refJ Casazza, P. G., Han, D., Larson, D. R.; Frames for Banach spaces; \CM; 247; 1999; 149--182; %CasazzaKovacevic03 % . 06jun04 \rhl{} \refJ Casazza, P., Kova\v cevi\'c, J.; Equal-norm tight frames with erasures; \AiCM; 18(2-4); 2003; 387--430; %CasciolaMorigi97 % larry 10sep99 \rhl{CM} \refP Casciola, G., Morigi, S.; Spline curves in polar and Cartesian coordinates; \ChamonixIIIa; 61--68; %CasciolaValori99 \rhl{C} \refR Casciola, G., Valori, G.; An inductive proof of the derivative B-spline recursion formula; Univ.\ of Bolgna; xxx; %Casey71a % Andreas Mueller 22may98 \rhl{C} \refJ Casey, J.; On cyclides and sphero--quartics; Phil.\ Trans.\ R. Soc.\ London; 161; 1871; 585--721; % The volume no is 161. %CashKarp90a \rhl{C} \refJ Cash, J. R., Karp, A. H.; A variable order Runge--Kutta method for initial value problems with rapidly varying right--hand side; \ACMTMS; 16; 1990; 201--222; %Casteljau00 % larry 20apr00 \rhl{} \refP Casteljau, Paul de Faget de; Intersections et convergence; \Stmalod; 9--15; %Casteljau59 \rhl{C} \refR Casteljau, P. de; Outillage m\'ethodes calcul; Andr\'e Citro\"en Automobiles SA, Paris; 1959; %Casteljau63 \rhl{C} \refR Casteljau, P. de; Courbes et Surfaces \`a P\^oles; Andr\'e Citro\"en Automobiles SA, Paris; 1963; %Casteljau85 \rhl{C} \refB Casteljau, P. de; Formes \`a P\^oles; Hermes (Paris); 1985; %Casteljau86 \rhl{C} \refB Casteljau, P. de; Shape Mathematics and CAD; Kogan PAGE Ltd (London); 1986; %Casteljau90a \rhl{C} \refB Casteljau, P. de; Le Lissage; Hermes (Paris); 1990; %Casteljau93 % carl \rhl{C} \refP Casteljau, Paul de; Polar forms for curve and surface modeling as used at Citro\"en; \Piegl; 1--12; % expository %Casteljau94 % larry \rhl{C} \refP Casteljau, P. de Faget de; Splines focales; \ChamonixIIa; 91--103; %Casteljau97 % larry 10sep99 \rhl{C} \rhl{C} \refP de Faget de Casteljau, P.; La tol\'erance d'usinage chez Citro\"en dans les ann\'ees (19)60; \ChamonixIIIa; 69--76; %Catmull74 \rhl{C} \refD Catmull, E. E.; A Subdivision Algorithm for Computer Display of Curved Surfaces; Computer Science Department, University of Utah; 1974; % also TR UTEC-CSc 74-133 %Catmull75 \rhl{C} \refQ Catmull, E.; Computer display of curved surfaces; (Proceedings, IEEE Conference on Computer Graphics, Pattern Recognition, and Data Structure, [Los Angeles]), xxx (ed.), xxx (xxx); 1975; 11--17; %CatmullClark78 % carl \rhl{C} \refJ Catmull, Edwin, Clark, J.; Recursively generated B-spline surfaces on arbitrary topological meshes; \CAD; 10(6); 1978; 350--355; %CatmullRom74 \rhl{C} \refP Catmull, E. E., Rom, R. J.; A class of local interpolating splines; \Barnhill; 317--326; %Cauchy40 % carl 23jun03 \rhl{Ca40} \refJ Cauchy, Augustin; Sur les fonctions interpolaires; \CRASP; 11; 1840; 775--789; % Oeuvres (1) 5, Paris: 1885: 409--424: % basic divided difference stuff, including a special case of the refinement % formula of Popoviciu33=34a %Cavaretta70 \rhl{C} \refD Cavaretta, A. S.; On cardinal perfect splines of least sup-norm on the real axis; Univ.\ Wis.; 1970; %Cavaretta73 % sonya \rhl{C} \refJ Cavaretta, A. S.; On cardinal perfect splines of least sup-norm on the real axis; \JAT; 8; 1973; 285--303; %Cavaretta74 % . 22may98 \rhl{C} \refJ Cavaretta, A. S.; An elementary proof of Kolmogorov's theorem; \AMMo; 81; 1974; 480--486; %Cavaretta76 % larry \rhl{C} \refJ Cavaretta, A. S.; One-sided inequalities for the successive derivatives of a function; \BAMS; 82; 1976; 303--305; %Cavaretta79 % author 29apr97 \rhl{C} \refJ Cavaretta, A. S.; A refinement of Kolmogorov's inequality; \JAT; 27; 1979; 45--60; %Cavaretta99c \rhl{C} \refR Cavaretta, A. S.; Oscillatory and zero properties for perfect splines and monosplines; xx; 19xx; %CavarettaDahmenMicchelli80 % . 14may99 \rhl{C} \refJ Cavaretta, A.~L., Micchelli, C.~A., Sharma, A.; Multivariate interpolation and the Radon transform; \MZ; 174; 1980; 263--279; %CavarettaDahmenMicchelli91 % carl \rhl{C} \refJ Cavaretta, A. S., Dahmen, W., Micchelli, C. A.; Stationary Subdivision; Mem.\ Amer.\ Math.\ Soc.; 93; 1991; No.\ 453; % vi+186 pp. %CavarettaDahmenMichelliSmith99 \rhl{C} \refJ Cavaretta, A. S., Dahmen, W., Micchelli, C. A., Smith, P. W.; A factorization theorem for band matrices; \LAA; xxx; xxx; xxx; %CavarettaGoodmanMicchelliSharma83 % sherm, shayne 23may95 6aug96 \rhl{C} \refJ Cavaretta, A. S., Goodman, T. N. T., Micchelli, C. A., Sharma, A.; Multivariate interpolation and the Radon transform, part III: Lagrange representation; \CMSCP; 3; 1983; 37--50; % More on lifting. Studies the choice of bases for the interpolation % conditions of maps from the family which Hakopian describes as the `scale % of mean value interpolations'. The points of interpolation must satisfy % certain geometric conditions, in which case the dual basis of `Lagrange % polynomials' is given. Related to Kergin interpolation. %CavarettaMicchelli89a % larry \rhl{C} \refP Cavaretta, A., Micchelli, C. A.; Subdivision algorithms; \Oslo; 115--153; %CavarettaMicchelli92 % author 20jun97 \rhl{C} \refP Cavaretta, A., Micchelli, C. A.; Pyramid patches provide potential polynomial paradigms; \Biri; 69--100; %CavarettaMicchelliSharma80a % larry, shayne 6aug96 \rhl{C} \refJ Cavaretta, A. S., Micchelli, C. A., Sharma, A.; Multivariate interpolation and the Radon transform; \MZ; 174; 1980; 263--279; % The first of three papers dealing with the lifting of univariate polynomial % valued projectors to multivariate maps by using the density of plane waves % includes Kergin interpolation which is the `lift' of Hermite interpolation %CavarettaMicchelliSharma80b % shayne 23may95 6aug96 \rhl{C} \refP Cavaretta, A. S., Micchelli, C. A., Sharma, A.; Multivariate interpolation and the Radon transform, part II: Some further examples; \BonnII; 49--61; % Additional examples of lifts of univariate maps, including Abel-Gontscharoff, % Lidstone, and the area matching interpolation maps. % Related to Kergin interpolation %CavarettaNewman78 \rhl{C} \refJ Cavaretta, A. S., Newman, D. J.; Periodic interpolating splines and their limits; Indag.\ Math.; 40; 1978; 515--526; %CavarettaSchoenberg72 % author 29apr97 \rhl{C} \refP Cavaretta, A., Schoenberg, I. J.; Solution of Landau's problem concerning higher derivatives on the halfline; \VarnaI; 297--308; %CavarettaSharmaTzimbalario86 % MR 08apr04 \rhl{} \refJ Cavaretta, A. S., Tzimbalario, J.; Convergence of some classes of interpolating splines for holomorphic functions; \JAT; 46(4); 1986; 374--384; % MR87j:30086 %CavarettaSharmaVarga81a % author 20feb96 \rhl{C} \refJ Cavaretta, A. S., Sharma, A., Varga, R. S.; Interpolation in the roots of unity: An extension of a theorem of Walsh; Resultate Math.; 3; 1981; 155--191; %CavarettaSitharam93 % carl \rhl{C} \refJ Cavaretta, A. S., Sitharam, Meera; The total variation of the tensor product Bernstein-B\'ezier operator; \JAT; 72(1); 1993; 34--39; %Cavendish74 % larry \rhl{C} \refJ Cavendish, J. C.; Automatic triangulation of arbitrary planar domains for the finite element method; Int.\ J. Numer.\ Meth.\ Engr.; 8; 1974; 679--696; %CaverettaDahmenMicchelli91 \rhl{C} \refB Caveretta, A., Dahmen, W., Micchelli, C.; Stationary Subdivision; Memoirs of AMS Number 453, American Mathematical Society (Providence); 1991; %Cayley73a \rhl{C} \refJ Cayley, A.; On the cyclide; Quart.\ J.\ Pure Appl.\ Math.; 12; 1873; 148--165; %Cea64 % larry \rhl{C} \refJ Cea, J.; Approximation variationnelle des problemes aux limites; Ann.\ Inst.\ Fourier, Grenoble; 14; 1964; 345--444; %CecchiMontani80 % larry \rhl{C} \refJ Cecchi, M. M., Montani, C.; Studio informatico della morfometria di un piccolo bacino in val d'era (Toscana); Atti Soc.\ Tosc.\ Sci.\ Nat.\ Mem.\ Ser.\ A; 87; 1980; 1--17; %CelnikerGossard91 \rhl{C} \refJ Celniker, G., Gossard, D.; Deformable curve and surface finite-elements for free-form shape design; Computer Graphics (ACM SIGGRAPH); 25; 1991; 257--266; %CerliencoMureddu % 12mar97 \rhl{C} \refJ Cerlienco, XXX., Mureddu, XXX.; XXX; Discrete Math.; 139; 1995; 73--87; % multivariate polynomial interpolation. % generate a monomially spanned space of minimal degree for interpolation at % a given point set in $\RR^d$. E.g., in the bivariate case, group points by % their first coordinate, then sort by decreasing group size to get the sets % $P_j$. The corresponding space is spanned by $( ()^k: k_1< \#P_{k_2} )$. %Cerny72 \rhl{C} \refJ Cerny, J. W.; Use of the SYMAP computer mapping program; J. Geography; 71; 1972; 167--174; %Chaikin74 \rhl{C} \refJ Chaikin, G. M.; An algorithm for high speed curve generation; Computer Graphics and Image Processing; 3; 1974; 346--349; %Chakalov34 % author 20jan03 \rhl{C34} \refJ Tchakaloff, L.; Sur la structure des ensembles lin\'eaires d\'efinis par une certaine propri\'et\'e minimale; Acta Math; 63; 1934; 77--97; % looks for minimal sets for given (n+1)-sequence tau and given function class % F, i.e., the smallest possible set E with the property that, % for every \xi in E there is some f in F with divdif{tau}f = D^nf(\xi)/n! . %Chakalov36a % carl 20jan03 \rhl{C36} \refJ Tchakaloff, L.; Sur une g\'en\'eralisation du th\'eor\`eme de Rolle pour les polynomes; \CRASP; 202; 1936; 1635--1637; % applies Chakalov34 to the special situation tau = (a,...,a,b,...,b), and % F = \Pi_k for some k \ge #tau. %Chakalov36b % carl 20jan03 \rhl{C36} \refJ Tchakaloff, L.; \"Uber eine Darstellung des Newtonschen Differenzenquotienten und ihre Anwendungen; Intern.\ Congr.\ Math., Oslo; 2; 1936; 98--99; % announcement of Chakalov38a,b %Chakalov38a % carl 20jan03 \rhl{C38a} \refJ Chakalov, L.; On a certain presentation of the Newton divided differences in interpolation theory and its applications (in Bulgarian); Annuaire Univ.\ Sofia, Fiz.\ Mat.\ Fakultet; 34; 1938; 353--394; % first occurrence of the contour integral formula for B-splines, % found later also by Meinardus74 % An extensive summary in German follows directly; see Chakalov38b %Chakalov38b % carl 20jan03 \rhl{C38b} \refJ Tschakaloff, L.; Eine Integraldarstellung des Newtonschen Differenzenquotienten und ihre Anwendungen; Annuaire Univ.\ Sofia, Fiz.\ Mat.\ Fakultet; 34; 1938; 395--405; % German summary of the Bulgarian paper Chakalov38a %ChalmersJohnsonMetcalfTaylor74 % carl \rhl{C} \refJ Chalmers, B. L., Johnson, D. J., Metcalf, F. T., Taylor, G. D.; Remarks on the rank of Hermite-Birkhoff interpolation; \SJNA; 11; 1974; 254--259; %ChalmersLeviatanProphet99 % carl 26aug99 \rhl{C} \refJ Chalmers, B. L., Leviatan, D., Prophet, M. P.; Optimal interpolating spaces preserving shape; \JAT; 98(2); 1999; 354--373; % spaces made up of solutions to variational problems involving shape % constraints in addition to interpolation constraints. %ChalmersMetcalf74 % shayne 5dec96 \rhl{C} \refJ Chalmers, B. L., Metcalf, F. T.; Taylor--like remainder formulas for interpolation by arbitrary linear functionals; \SJNA; 11(5); 1974; 950--964; %ChalmersMetcalf76 % author 20apr00 \rhl{CM} \refP Chalmers, B. L., Metcalf, F. T.; On the computation of minimal projections from $C[0,1]$ to ${\cal P}_n[0,1]$; \TexasII; 321--326; %ChalmersMetcalf80 % author 20apr00 \rhl{CM} \refP Chalmers, B. L., Metcalf, F. T.; Multiplicative variations lead to the variational equations for minimal projections; \TexasIII; xxx--xxx; %ChalmersMetcalf90 % petras 20apr00 \rhl{CM} \refJ Chalmers, B. L., Metcalf, F. T.; Determination of a minimal projection from $C[-1,1]$ onto the quadratics; \NFAO; 11(1-2); 1990; 1--10; % in preparation since mid 1970ies %ChalmersPhillipsTaylor88 % shayne 5dec96 \rhl{C} \refJ Chalmers, B. L., Phillips, G. M., Taylor, P. J.; Polynomial approximation using projections whose kernels contain the Chebyshev polynomials; \JAT; 53 ; 1988; 321--334; % Bruce Chalmers writes: % In Theorem 2.1 P is definitely assumed to be a linear map. I have no % idea what happens if the assumption of linearity is dropped. Also % Theorem 3.4 is in error (in the proof the conclusion that \nu is a % positive measure does not follow). In fact the whole half page % beginning with Theorem 3.4 until the beginning of Section 4 should % be eliminated. In the proof of Theorem 2.3 in the second sentence % "f" should be replaced by "f-Pf" throughout (4 places). Finally, % in the statement of Theorem 3.2, replace "nonnegative" by % "absolutely continuous" and after "satisfying" insert % "0<=d\nu/dt<=1," %ChalmondColdefyLavayssiere94 % larry \rhl{C} \refP Chalmond, B., Coldefy, F., Lavayssi\`ere, B.; 3D curve reconstruction from degraded projections; \ChamonixIIb; 113--119; %Chamayou75 \rhl{C} \refJ Chamayou, J. M.; Bicubic spline function approximation of the solution of the fast-neutron transport equation; Comp.\ Phys.\ Comm.; 10; 1975; 282--291; %ChampionLenardMills00 % Terry Mills 21jan02 \rhl{} \refJ Champion, R., Lenard, C. T., Mills, T. M.; A variational approach to splines; ANZIAM Journal; 42; 2000; 119--135; % This is an expository paper which describes the development of a % variational approach to spline functions. %ChampionLenardMills96 % Terry Mills 12mar97 \rhl{C} \refJ Champion, R., Lenard, C. T., Mills, T. M.; An introduction to abstract splines; Math.\ Scientist; 21; 1996; 8--26; % An exposition of some basic ideas in the study of % variational splines %ChanTFKangSHShenJ02 % author 20nov03 \rhl{} \refJ Chan, T. F., Kang, S.-H., Shen, J.; Euler's elastica and curvature based inpaintings; \SJAM; 63(2); 2002; 564--592; % minimize int_\gO (a+b\gk^2)|Du|, with \gk:= \nabla\cdot|grad u/|grad u|| %ChanYeung92 % carl \rhl{C} \refJ Chan, Raymond H., Yeung, Man-Chung; Jackson's theorem and circulant preconditioned Toeplitz systems; \JAT; 70; 1992; 191--205; %Chand65 \rhl{C} \refD Chand, D. R.; Appproximation of curves by piecewise continuous functions; Boston Univ.; 1965; %ChandlerSloan90 % carl \rhl{C} \refJ Chandler, G. A., Sloan, I. H.; Spline qualocation methods for boundary integral equations; \NM; 58; 1990; 537--567; %ChandlerSloan90a % . 05feb96 \rhl{C} \refJ Chandler, G. A., Sloan, I. H.; Spline qualocation methods for boundary integral equations; \NM; 58; 1990; 537--567; % erratum: \NM: 62: 1992: 295 %ChandlerSloan92 % carl \rhl{C} \refJ Chandler, G. A., Sloan, I. H.; Erratum: Spline qualocation methods for boundary integral equations; \NM; 62; 1992; 295; %ChandruDuttaHoffmann89a \rhl{C} \refJ Chandru, V., Dutta, D., Hoffmann, C. M.; On the geometry of Dupin cyclides; The Visual Computer; 5; 1989; 277--290; %ChandruDuttaHoffmann90a \rhl{C} \refQ Chandru, V., Dutta, D., Hoffmann, C. M.; Variable radius blending using Dupin cyclides; (Geometric Modeling for Product Engineering), M. J. Wozny, J. Turner and K. Preiss (eds.), North-Holland, (xxx); 1990; xxx; %ChandruKochar87a \rhl{C} \refP Chandru, Kochar; Analytic techniques for geometric intersection problems; \Troy; 316--317; %Chang82a % . 5dec96 \rhl{C} \refJ Chang, G.; Matrix foundation of Bezier technique; \CAD; 14(6); 1982; 354--360; % page numbers are doubtful. %Chang84 % Shayne 22may98 \rhl{C} \refJ Chang, G.-Z.; Bernstein polynomials via the shifting operator; \AMMo; 91; 1984; 634--638; %Chang94 % . \rhl{C} \refJ Chang, Maoli; The behavior of polyharmonic cardinal splines as their degree tends to infinity; \JAT; 76(3); 1994; 287--302; %ChangChen91 % LLS Lai-Schumaker book \rhl{ChaC91} \refJ Chang, G. Z., Chen, F. L.; A short proof of a converse theorem of convexity for Bernstein polynomials over simplices (Chinese); J. Math.\ Res.\ Exposition; 11; 1991; 275--277; %ChangFeng89 % LLS Lai-Schumaker book \rhl{ChaF89} \refJ Chang, G. Z., Feng, Y. Y.; A pair of compatible variations for Bernstein triangular polynomials; \ATA; 5; 1989; 1--10; %ChangG83 % larry \rhl{C} \refJ Chang, G. Z.; Generalized Bernstein B\'ezier polynomials; J. Comput.\ Math.; 1; 1983; 322--327; %ChangG84a % larry 20jun97 \rhl{C} \refJ Chang, Gen-zhe; An elementary proof of the convergence for the generalized Bernstein B\'ezier polynomials; \JCM; 2; 1984; 89--92; %ChangG99a % carl \rhl{C} \refJ Chang, Gen-zhe; Matrix formulations of B\'ezier technique; \CAD; xx; xx; 345--350; %ChangGDavis84a % sonya \rhl{C} \refJ Chang, Gen-zhe, Davis, P. J.; The convexity of Bernstein polynomials over triangles; \JAT; 40; 1984; 11--28; %ChangGFeng83a % \rhl{C} \refJ Chang, Gen-zhe, Feng, Yu-yu; Error bound for Bernstein-B\'ezier triangular approximations; J.\ Comput.\ Math.; 4; 1983; 335--340; %ChangGFeng84a % greg \rhl{C} \refJ Chang, Gen-zhe, Feng, Yu-yu; An improved condition for the convexity of Bernstein-B\'ezier surfaces over triangles; \CAGD; 1; 1984; 279--283; %ChangGFeng85a \rhl{C} \refR Chang, Gen-zhe, Feng, Yu-yu; A pair of compatible variations for Bernstein triangular polynomials; xx; 1985; %ChangGFeng85b % larry \rhl{C} \refJ Chang, Gen-zhe, Feng, Yu-yu; A new proof for the convexity of the Bernstein-B\'ezier surfaces over triangles; Chin.\ Ann.\ of Math.; 6B; 1985; 171--176; % some have 173--176 %ChangGHoschek85a \rhl{C} \refP Chang, Gen-zhe, Hoschek, J.; Convexity and variation diminishing property of Bernstein polynomials over triangles; \MvatIII; 61--71; %ChangGSu85 % greg \rhl{C} \refJ Chang, G., Su, B.; Families of adjoint patches for a B\'ezier triangular surface; \CAGD; 2; 1985; 37--42; %ChangGWu81 % carl \rhl{C} \refJ Chang, Gengzhe, Wu, Junheng; Mathematical foundations of B\'ezier's technique; \CAD; 13(3); 1981; 134--136; %ChangGZhang90 % sonya \rhl{C} \refJ Chang, G., Zhang, J.; Converse theorems of convexity for Bernstein polynomials over triangles; \JAT; 61; 1990; 265--278; %ChangR80 \rhl{C} \refR Chang, R. E.; An evaluation and comparison of curve fitting software; SAND80--8727; 1980; %ChangSederberg94 % LLS Lai-Schumaker book \rhl{ChaS94} \refJ Chang, G. Z., Sederberg, T.; Nonnegative quadratic B\'ezier triangular patches; \CAGD; 11; 1994; 113--116; %ChangZ82 \rhl{C} \refJ Chang, Z. X; Vectorial splines.\ Interpolation type operators and surface fitting by vectorial splines (Chinese); Xian Jiaotoug Daxue Xuebao; 16; 1982; 41--52; %ChapuisCorrec99 \rhl{C} \refJ Chapuis, E., Correc, Y.; Fast computation of Delaunay triangulations; Advances in Engineering Software; XX; XX; XX; %CharrotGregory84 % greg \rhl{C} \refJ Charrot, P., Gregory, J. A.; A pentagonal surface patch for computer aided geometric design; \CAGD; 1; 1984; 87--94; %ChatterjeeDikshit81a % . 20feb96 \rhl{C} \refJ Chatterjee, A., Dikshit, H. P.; On error bounds for cubic spline interpolation; J. Orissa Math.\ Soc.; 1; 1982; 1--11; %ChatterjeeDikshit81b % . 20feb96 \rhl{C} \refJ Chatterjee, A., Dikshit, H. P.; Convergence of a class of cubic interpolatory splines; \PAMS; 82; 1981; 411--416; %Chazelle92 % sherm, update pagination \rhl{C} \refJ Chazelle, Bernard; An optimal algorithm for intersecting three-dimensional convex polyhedra; \SJC; 21(4); 1992; 671--696; %Chen81c \rhl{C} \refJ Han-Lin, C.; Complex spline functions; Scientia Sinica; 24; 1981; 160--169; %Chen94a % carl \rhl{C} \refJ Chen, Dirong; Best one-sided approximation of convolution classes by cardinal splines; \JATA; 10(4); 1994; 110--117; %Chen95a % carl \rhl{C} \refJ Chen, Debao; Spline wavelets of small support; \SJMA; 26(2); 1995; 500--517; % certain dilated derivatives of a cardinal B-spline, e.g., % $(D^{k}N)(2\cdot| 0,\ldots, m+k)$ or $(D^{k}N)(2\cdot-1| 0,\ldots, m+k)$, is % a wavelet %ChenDR94a % carl \rhl{C} \refJ Chen, Di-rong; Perfect splines with boundary conditions of least norm; \JAT; 77; 1994; 191--201; %ChenDitzian90a % shayne 14sep95 \rhl{C} \refJ Chen, W., Ditzian, Z.; Mixed and directional derivatives; \PAMS; 108; 1990; 177--185; % main result relies on a generalisation of a result of %Kellogg28 % Shayne has written a note about this %ChenF95 % carl 19nov95 \rhl{C} \refJ Chen, Falai; The best Lipschitz constants of Bernstein polynomials and Bezier nets over a given triangle; \JATA; 11(2); 1995; 1--8; % shape preserving %ChenFeng93 % shayne 22may98 \rhl{C} \refJ Chen, Fa Lai, Feng, Yu Yu; Limit of iterates for Bernstein polynomials defined on a triangle; Appl.{} Math.{} J. Chinese Univ.\ Ser.\ B ; 8; 1993; 45--53; %ChenFengKozak97 % J. Kozak 14may99 \rhl{C} \refJ Chen, F., Feng, Y. Y., Kozak, J.; Tracing a planar algebraic curve; Applied Mathematics - A Journal of Chinese Universities; 12; 1997; 15--24; %ChenG87 \rhl{C} \refD Chen, G.; Spline approach to optimal control problems with constraints; Texas A\&M Univ.; 1987; %ChenG89 \rhl{C} \refR Chen, G.; Optimal recovery of certain nonlinear analytic mappings; Rice Univ.; 1989; %ChenG99 \rhl{C} \refR Chen, G.; Reproducing kernel structure of thin plate splines over a circular domain with boundary conditions; xx; 19xx; %ChenGChuiLaiMJ88a % . 20apr99 \rhl{CCL} \refJ Chen, G., Chui, C. K., Lai, M. J.; Construction of real-time spline quasi-interpolation schemes; \ATA; 4; 1988; 61--75; % CAT 107: 1986: %ChenHL00 % . 20apr00 \rhl{} \refB Chen, Han-lin; Complex Harmonic Splines, Periodic Quasi-Waveletes: Theory and Applications; Kluwer Academy Publisher (Netherlands); 2000; % http://www.wkap.nl/book.htm/0-7923-6137-7 %ChenHL78 \rhl{C} \refJ Chen, H. L.; The order of error bounds for cubic spline functions (Chinese); Acta Math.\ Appl.\ Sinica ; 1; 1978; 42--58; %ChenHL80 \rhl{C} \refR Chen, Han-Lin; Interpolation and approximation on the unit circle, Part I; Trondheim; 1980; %ChenHL81 \rhl{C} \refR Chen, Han-Lin; Complex Harmonic Splines: Interpolation and approximation on the unit circle, Part II; Trondheim; 1981; %ChenHL81b \rhl{C} \refR Chen, Han-Lin; The zeros of rational splines and complex splines; Trondheim; 1981; %ChenHL81c % . 10nov97 \rhl{C} \refJ Chen, Han-Lin; Complex spline functions; Scientia Sinica; 24; 1981; 160--169; %ChenHL82 \rhl{C} \refR Chen, H. L.; Interpolation by splines on finite and infinite planar sets; Beijing; 1982; %ChenHL83a % sonya \rhl{C} \refJ Chen, Han Lin; The zeros of rational splines and complex splines; \JAT; 39; 1983; 308--319; %ChenHL83b % sonya \rhl{C} \refJ Chen, H. L.; Quasi interpolating splines on the unit circle; \JAT; 38; 1983; 312--318; %ChenHL84 \rhl{C} \refR Chen, H. L.; On the uniqueness of the extremal function of Landau type problem for the differential operator $L_{n1}$; Beijing; 1984; %ChenHL85 % sonya \rhl{C} \refJ Chen, H. L.; Interpolation and approximation on the unit disk by complex harmonic splines; \JAT; 43; 1985; 112--123; %ChenHL85b \rhl{C} \refR Chen, H. L.; Some extremal problems; Beijing; 1985; %ChenHLChui93a % sherm \rhl{C} \refJ Chen, Han-Lin, Chui, C. K.; On a generalized Euler spline and its applications to the study of convergence in cardinal interpolation and solutions of certain extremal problems; \AMASH; 61; 1993; 219--233; %ChenKozak94 % J. Kozak 14may99 \rhl{C} \refJ Chen, F., Kozak, J.; The intersection of a triangular patch and a plane; \JCM; 12; 1994; 138--146; %ChenKozak96 % J. Kozak 14may99 \rhl{C} \refJ Chen, F., Kozak, J.; On computing zeros of a bivariate Bernstein polynomial; \JCM; 14; 1996; 237--248; %ChenLi94 % carl \rhl{C} \refJ Chen, Hongsen, Li, Bo; Superconvergence analysis and error expansion for the Wilson nonconforming finite element; \NM; 69(2); 1994; 125--140; % optimal error, Wilson's brick, Irons patch test %ChenT99 \rhl{C} \refR Chen, T.; Asymptotic expansion for splines; Fudan; 19xx; %ChenTChenHLiu91 \rhl{C} \refQ Chen, T., Chen, H., Liu, R.; A constructive proof and extension of Cybenko's approximation theorem; (Computing Science and Statistics), xxx (ed.), Proceedings of the 22nd Symposium on the Interface, Springer-Verlag (New York); 1991; 163--168; %ChenTP80 \rhl{C} \refJ Chen, T. P.; Spline functions (Chinese); Acta Math.\ Apl.\ Sinica; 3; 1980; 41--49; %ChenTP80b \rhl{C} \refJ Chen, T. P.; On Varma's lacunary interpolation by splines (Chinese); Chinese Ann.\ Math.; 1; 1980; 75--82; %ChenTP81 \rhl{C} \refJ Chen, T. P.; On some kinds of lacunary interpolation spline; Acta.\ Math.\ Appl.\ Sin.; 4; 1981; 253--257; %ChenTP81b \rhl{C} \refJ Chen, T. P.; On error bounds for splines (Chinese); Fudan Daxue Xueobao; 20; 1981; 15--22; %ChenTP81c \rhl{C} \refJ Chen, T. P.; On lacunary interpolating splines; Sci.\ Sinica; 24; 1981; 606--617; %ChenTP81d \rhl{C} \refJ Chen, T. P.; A class of quintic lacunary interpolation splines with nonuniform mesh (Chinese); Chinese Ann.\ Math; 2; 1981; 311--318; %ChenTP82 \rhl{C} \refJ Chen, T. P.; Error estimates and asymptotic expansion for Hermite splines (Chinese); Fudan Xuebao; 4; 1982; 423--432; %ChenTP83 \rhl{C} \refJ Chen, T. P.; Structural properties of functions described by splines (Chinese); Chinese Ann.\ Math.\ Ser.\ A; 4; 1983; 379--383; %ChenWLouck96a % carl 20nov03 \rhl{} \refJ Chen, William Y. C., Louck, James; Interpolation for symmetric functions; \AiM; 117; 1996; 147--156; % generalization of Lagrange formula; % Let x_1,\ldots,x_n distinct points in \RR, let 0