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## Alfeld, Peter

Compute Distance To:
 Author ID: alfeld.peter Published as: Alfeld, P.; Alfeld, Peter External Links: MGP · Wikidata
 Documents Indexed: 45 Publications since 1977
all top 5

#### Co-Authors

 16 single-authored 21 Schumaker, Larry L. 4 Neamtu, Marian 3 Eyre, David J. 3 Piper, Bruce 3 Sirvent, Maritza 3 Sorokina, Tatyana 1 Barnhill, Robert E. 1 Lambert, J. D. 1 Whiteley, Walter John
all top 5

#### Serials

 7 Mathematics of Computation 7 Computer Aided Geometric Design 5 SIAM Journal on Numerical Analysis 3 Advances in Computational Mathematics 2 Rocky Mountain Journal of Mathematics 2 ACM Transactions on Mathematical Software 2 Journal of Approximation Theory 2 Journal of Computational and Applied Mathematics 2 Numerische Mathematik 2 Constructive Approximation 2 SIAM Journal on Mathematical Analysis 1 BIT 1 Approximation Theory and its Applications

#### Fields

 33 Approximations and expansions (41-XX) 30 Numerical analysis (65-XX) 1 Functions of a complex variable (30-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Computer science (68-XX)

#### Citations contained in zbMATH

40 Publications have been cited 499 times in 262 Documents Cited by Year
The dimension of bivariate spline spaces of smoothness r for degree $$d\geq 4r+1$$. Zbl 0646.41008
Alfeld, Peter; Schumaker, L. L.
1987
Fitting scattered data on sphere-like surfaces using spherical splines. Zbl 0863.65002
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1996
An explicit basis for $$C^ 1$$ quartic bivariate splines. Zbl 0658.65008
Alfeld, Peter; Piper, Bruce; Schumaker, L. L.
1987
A trivariate Clough-Tocher scheme for tetrahedral data. Zbl 0566.65003
Alfeld, Peter
1984
Bernstein-Bézier polynomials on spheres and sphere-like surfaces. Zbl 0875.68863
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1996
On the dimension of bivariate spline spaces of smoothness r and degree $$d=3r+1$$. Zbl 0725.41012
Alfeld, Peter; Schumaker, Larry L.
1990
A bivariate $$C^ 2$$ Clough-Tocher scheme. Zbl 0597.65005
Alfeld, Peter
1984
Smooth macro-elements based on Powell–Sabin triangle splits. Zbl 0993.65124
Alfeld, Peter; Schumaker, Larry L.
2002
Smooth macro-elements based on Clough-Tocher triangle splits. Zbl 0998.65016
Alfeld, Peter; Schumaker, Larry L.
2002
Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree $$d\geq 4r+1$$. Zbl 0668.41011
Alfeld, Peter; Piper, Bruce; Schumaker, L. L.
1987
Circular Bernstein-Bézier polynomials. Zbl 0835.30001
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1995
Bivariate spline spaces and minimal determining sets. Zbl 0966.65017
Alfeld, Peter
2000
Dimension and local bases of homogeneous spline spaces. Zbl 0854.41030
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1996
The generic dimension of the space of $$C^ 1$$ splines of degree $$d\geq 8$$ on tetrahedral decompositions. Zbl 0774.41012
Alfeld, Peter; Schumaker, Larry L.; Whiteley, Walter
1993
On dimension and existence of local bases for multivariate spline spaces. Zbl 0761.41007
Alfeld, Peter; Schumaker, Larry L.; Sirvent, Maritza
1992
Derivative generation from multivariate scattered data by functional minimization. Zbl 0585.65014
Alfeld, Peter
1985
Multivariate perpendicular interpolation. Zbl 0588.65004
Alfeld, Peter
1985
On the dimension of multivariate piecewise polynomials. Zbl 0655.41010
Alfeld, P.
1986
A discrete $$C^ 1$$ interpolant for tetrahedral data. Zbl 0566.65004
Alfeld, Peter
1984
Correction in the dominant space: A numerical technique for a certain class of stiff initial value problems. Zbl 0391.65031
Alfeld, P.; Lambert, J. D.
1977
Linear differential operators on bivariate spline spaces and spline vector fields. Zbl 1342.41010
Alfeld, Peter; Sorokina, Tatyana
2016
Scattered data interpolation in three or more variables. Zbl 0682.41003
Alfeld, Peter
1989
A $$C^2$$ trivariate macroelement based on the Worsey–Farin split of a tetrahedron. Zbl 1097.65031
Alfeld, Peter; Schumaker, Larry L.
2005
Upper and lower bounds on the dimension of multivariate spline spaces. Zbl 0849.41027
Alfeld, Peter
1996
A transfinite $$C^ 2$$ interpolant over triangles. Zbl 0558.65002
Alfeld, Peter; Barnhill, Robert E.
1984
Upper and lower bounds on the dimension of superspline spaces. Zbl 1012.41012
Alfeld, Peter; Schumaker, Larry L.
2003
The structure of multivariate superspline spaces of high degree. Zbl 0742.41012
Alfeld, Peter; Sirvent, Maritza
1991
Two tetrahedral $$C^1$$ cubic macro elements. Zbl 1173.41005
Alfeld, Peter; Sorokina, Tatyana
2009
Bounds on the dimensions of trivariate spline spaces. Zbl 1159.41002
Alfeld, Peter; Schumaker, Larry L.
2008
A $$C^2$$ trivariate macro-element based on the Clough-Tocher-split of a tetrahedron. Zbl 1084.65016
Alfeld, Peter; Schumaker, Larry L.
2005
A $$C^2$$ trivariate double-Clough-Tocher macro-element. Zbl 1074.65020
Alfeld, Peter; Schumaker, Larry L.
2005
Spaces of bivariate splines on triangulations with holes. Zbl 0687.41017
Alfeld, P.; Piper, B.; Schumaker, L. L.
1987
Nonexistence of star-supported spline bases. Zbl 0957.41006
Alfeld, Peter; Schumaker, Larry L.
2000
A recursion formula for the dimension of super spline spaces of smoothness r and degree $$d>r2^ k$$. Zbl 0682.41024
Alfeld, Peter; Sirvent, Maritza
1989
Inverse linear multistep methods for the numerical solution of initial value problems of ordinary differential equations. Zbl 0408.65048
Alfeld, Peter
1979
Multivariate splines and the Bernstein-Bézier form of a polynomial. Zbl 1418.41003
Alfeld, Peter
2016
Two condensed macro-elements with full approximation power. Zbl 1190.41003
Alfeld, Peter; Schumaker, Larry L.; Sorokina, Tatyana
2010
The exact analysis of sparse rectangular linear systems. Zbl 0900.65109
Alfeld, Peter; Eyre, David J.
1991
Fixed point iteration with inexact function values. Zbl 0481.65026
Alfeld, Peter
1982
A special class of explicit linear multistep methods as basic methods for the correction in the dominant space technique. Zbl 0445.65073
Alfeld, Peter
1979
Linear differential operators on bivariate spline spaces and spline vector fields. Zbl 1342.41010
Alfeld, Peter; Sorokina, Tatyana
2016
Multivariate splines and the Bernstein-Bézier form of a polynomial. Zbl 1418.41003
Alfeld, Peter
2016
Two condensed macro-elements with full approximation power. Zbl 1190.41003
Alfeld, Peter; Schumaker, Larry L.; Sorokina, Tatyana
2010
Two tetrahedral $$C^1$$ cubic macro elements. Zbl 1173.41005
Alfeld, Peter; Sorokina, Tatyana
2009
Bounds on the dimensions of trivariate spline spaces. Zbl 1159.41002
Alfeld, Peter; Schumaker, Larry L.
2008
A $$C^2$$ trivariate macroelement based on the Worsey–Farin split of a tetrahedron. Zbl 1097.65031
Alfeld, Peter; Schumaker, Larry L.
2005
A $$C^2$$ trivariate macro-element based on the Clough-Tocher-split of a tetrahedron. Zbl 1084.65016
Alfeld, Peter; Schumaker, Larry L.
2005
A $$C^2$$ trivariate double-Clough-Tocher macro-element. Zbl 1074.65020
Alfeld, Peter; Schumaker, Larry L.
2005
Upper and lower bounds on the dimension of superspline spaces. Zbl 1012.41012
Alfeld, Peter; Schumaker, Larry L.
2003
Smooth macro-elements based on Powell–Sabin triangle splits. Zbl 0993.65124
Alfeld, Peter; Schumaker, Larry L.
2002
Smooth macro-elements based on Clough-Tocher triangle splits. Zbl 0998.65016
Alfeld, Peter; Schumaker, Larry L.
2002
Bivariate spline spaces and minimal determining sets. Zbl 0966.65017
Alfeld, Peter
2000
Nonexistence of star-supported spline bases. Zbl 0957.41006
Alfeld, Peter; Schumaker, Larry L.
2000
Fitting scattered data on sphere-like surfaces using spherical splines. Zbl 0863.65002
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1996
Bernstein-Bézier polynomials on spheres and sphere-like surfaces. Zbl 0875.68863
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1996
Dimension and local bases of homogeneous spline spaces. Zbl 0854.41030
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1996
Upper and lower bounds on the dimension of multivariate spline spaces. Zbl 0849.41027
Alfeld, Peter
1996
Circular Bernstein-Bézier polynomials. Zbl 0835.30001
Alfeld, Peter; Neamtu, Marian; Schumaker, Larry L.
1995
The generic dimension of the space of $$C^ 1$$ splines of degree $$d\geq 8$$ on tetrahedral decompositions. Zbl 0774.41012
Alfeld, Peter; Schumaker, Larry L.; Whiteley, Walter
1993
On dimension and existence of local bases for multivariate spline spaces. Zbl 0761.41007
Alfeld, Peter; Schumaker, Larry L.; Sirvent, Maritza
1992
The structure of multivariate superspline spaces of high degree. Zbl 0742.41012
Alfeld, Peter; Sirvent, Maritza
1991
The exact analysis of sparse rectangular linear systems. Zbl 0900.65109
Alfeld, Peter; Eyre, David J.
1991
On the dimension of bivariate spline spaces of smoothness r and degree $$d=3r+1$$. Zbl 0725.41012
Alfeld, Peter; Schumaker, Larry L.
1990
Scattered data interpolation in three or more variables. Zbl 0682.41003
Alfeld, Peter
1989
A recursion formula for the dimension of super spline spaces of smoothness r and degree $$d>r2^ k$$. Zbl 0682.41024
Alfeld, Peter; Sirvent, Maritza
1989
The dimension of bivariate spline spaces of smoothness r for degree $$d\geq 4r+1$$. Zbl 0646.41008
Alfeld, Peter; Schumaker, L. L.
1987
An explicit basis for $$C^ 1$$ quartic bivariate splines. Zbl 0658.65008
Alfeld, Peter; Piper, Bruce; Schumaker, L. L.
1987
Minimally supported bases for spaces of bivariate piecewise polynomials of smoothness r and degree $$d\geq 4r+1$$. Zbl 0668.41011
Alfeld, Peter; Piper, Bruce; Schumaker, L. L.
1987
Spaces of bivariate splines on triangulations with holes. Zbl 0687.41017
Alfeld, P.; Piper, B.; Schumaker, L. L.
1987
On the dimension of multivariate piecewise polynomials. Zbl 0655.41010
Alfeld, P.
1986
Derivative generation from multivariate scattered data by functional minimization. Zbl 0585.65014
Alfeld, Peter
1985
Multivariate perpendicular interpolation. Zbl 0588.65004
Alfeld, Peter
1985
A trivariate Clough-Tocher scheme for tetrahedral data. Zbl 0566.65003
Alfeld, Peter
1984
A bivariate $$C^ 2$$ Clough-Tocher scheme. Zbl 0597.65005
Alfeld, Peter
1984
A discrete $$C^ 1$$ interpolant for tetrahedral data. Zbl 0566.65004
Alfeld, Peter
1984
A transfinite $$C^ 2$$ interpolant over triangles. Zbl 0558.65002
Alfeld, Peter; Barnhill, Robert E.
1984
Fixed point iteration with inexact function values. Zbl 0481.65026
Alfeld, Peter
1982
Inverse linear multistep methods for the numerical solution of initial value problems of ordinary differential equations. Zbl 0408.65048
Alfeld, Peter
1979
A special class of explicit linear multistep methods as basic methods for the correction in the dominant space technique. Zbl 0445.65073
Alfeld, Peter
1979
Correction in the dominant space: A numerical technique for a certain class of stiff initial value problems. Zbl 0391.65031
Alfeld, P.; Lambert, J. D.
1977
all top 5

#### Cited by 305 Authors

 21 Schumaker, Larry L. 18 Alfeld, Peter 15 Sorokina, Tatyana 9 Lai, Mingjun 9 Speleers, Hendrik 8 Nürnberger, Günther 8 Schenck, Hal 8 Zeilfelder, Frank 7 Wang, Renhong 6 Zhang, Shangyou 5 Chui, Charles Kam-tai 5 Mraoui, Hamid 5 Neamtu, Marian 4 Dipasquale, Michael R. 4 Guzmán, Johnny 4 Lamnii, Abdelleh 4 Lyche, Tom 4 Mourrain, Bernard 4 Pham, Duong Thanh 4 Sbibih, Driss 4 Šír, Zbyněk 3 Deng, Jiansong 3 Dierckx, Paul 3 Farin, Gerald E. 3 Gravesen, Jens 3 Grošelj, Jan 3 Hong, Don 3 Kosinka, Jiří 3 Le Méhauté, Alain J. Y. 3 Manni, Carla 3 Matt, Michael Andreas 3 Neilan, Michael 3 Qian, Xiaoping 3 Sánchez-Reyes, Javier 3 Stillman, Michael Eugene 3 Tijini, Ahmed 3 Vandewalle, Stefan G. 3 Worsey, Andrew J. 2 Baramidze, Victoria 2 Barton, Michael H. 2 Billera, Louis J. 2 Chen, Falai 2 Chernov, Alexey 2 Davydov, Oleg V. 2 De Marchi, Stefano 2 Dişibüyük, Çetin 2 Floater, Michael S. 2 Foley, Thomas A. 2 Gao, Junbin 2 Goldman, Ron N. 2 Grandine, Thomas A. 2 Han, Danfu 2 Hecklin, Gero 2 Hesse, Kerstin 2 Hu, Jun 2 Hu, Kaibo 2 Jaklič, Gašper 2 Jüttler, Bert 2 Krajnc, Marjeta 2 Laghchim-Lahlou, Mohammed 2 Lamnii, M. 2 Lang, Feng-Gong 2 Lavery, John E. 2 Lávička, Miroslav 2 Le, Tung 2 Li, Chongjun 2 Liu, Huan-Wen 2 Liu, Huanwen 2 Luo, Zhongxuan 2 McDonald, Terry 2 Muntingh, Georg 2 Pesenson, Isaac Zalmanovich 2 Rescorla, K. L. 2 Rössl, Christian 2 Seidel, Hans-Peter 2 Sha, O. P. 2 Sharma, Ravi K. 2 Shi, Xiquan 2 Sloan, Ian Hugh 2 Tohǎneanu, Ştefan O. 2 Toshniwal, Deepesh 2 Tran, Than 2 Villamizar, Nelly 2 Vršek, Jan 2 Wang, Tianjun 2 Womersley, Robert S. 2 Xia, Songtao 2 Xu, Gang 2 Xu, Jinchao 2 Yin, Baocai 1 Aluie, Hussein 1 Anders, Katie 1 Anderson, Leonard R. 1 Angoshtari, Arzhang 1 Barnhill, Robert E. 1 Barros, Saulo R. M. 1 Beccari, Carolina Vittoria 1 Beliakov, Gleb 1 Bernstein, Swanhild 1 Bizzarri, Michal ...and 205 more Authors
all top 5

#### Cited in 67 Serials

 56 Computer Aided Geometric Design 42 Journal of Computational and Applied Mathematics 17 Journal of Approximation Theory 16 Mathematics of Computation 11 Advances in Computational Mathematics 10 Computers & Mathematics with Applications 9 Constructive Approximation 8 Numerische Mathematik 7 Computer Methods in Applied Mechanics and Engineering 5 Advances in Applied Mathematics 5 Applied Numerical Mathematics 4 BIT 4 Computing 3 Applied Mathematics and Computation 3 Numerical Algorithms 2 Journal of Computational Physics 2 Rocky Mountain Journal of Mathematics 2 Calcolo 2 Journal of Pure and Applied Algebra 2 Results in Mathematics 2 SIAM Journal on Numerical Analysis 2 Journal of Complexity 2 GEM - International Journal on Geomathematics 1 Applicable Analysis 1 International Journal for Numerical Methods in Fluids 1 Journal of Mathematical Analysis and Applications 1 Acta Mathematica Vietnamica 1 Journal of Algebra 1 Journal of the American Statistical Association 1 Manuscripta Mathematica 1 Monatshefte für Mathematik 1 Pacific Journal of Mathematics 1 Rendiconti del Seminario Matemàtico e Fisico di Milano 1 Theoretical Computer Science 1 Transactions of the American Mathematical Society 1 Optimal Control Applications & Methods 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Journal of Symbolic Computation 1 Discrete & Computational Geometry 1 Numerical Methods for Partial Differential Equations 1 Mathematical and Computer Modelling 1 Science in China. Series A 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 Applied Mathematical Modelling 1 European Journal of Operational Research 1 International Journal of Computer Mathematics 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 Linear Algebra and its Applications 1 Computers and Mathematics with Applications. Part B 1 Computational Optimization and Applications 1 Applied Mathematics. Series B (English Edition) 1 The Journal of Fourier Analysis and Applications 1 Mathematical Inequalities & Applications 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Engineering Computations 1 Brazilian Journal of Probability and Statistics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 International Journal of Numerical Analysis and Modeling 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Communications in Applied Mathematics and Computational Science 1 Mathematics in Computer Science 1 Inverse Problems and Imaging 1 Electronic Journal of Statistics 1 Axioms 1 Journal of Mathematics 1 SMAI Journal of Computational Mathematics 1 Communications on Applied Mathematics and Computation
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#### Cited in 38 Fields

 190 Numerical analysis (65-XX) 151 Approximations and expansions (41-XX) 17 Computer science (68-XX) 16 Commutative algebra (13-XX) 12 Partial differential equations (35-XX) 11 Convex and discrete geometry (52-XX) 8 Fluid mechanics (76-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Special functions (33-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Geophysics (86-XX) 3 Algebraic geometry (14-XX) 3 Functional analysis (46-XX) 3 Algebraic topology (55-XX) 3 Statistics (62-XX) 3 Mechanics of deformable solids (74-XX) 2 Combinatorics (05-XX) 2 Category theory; homological algebra (18-XX) 2 Ordinary differential equations (34-XX) 2 Abstract harmonic analysis (43-XX) 2 Integral transforms, operational calculus (44-XX) 2 Integral equations (45-XX) 2 Manifolds and cell complexes (57-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 Field theory and polynomials (12-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Operations research, mathematical programming (90-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)

#### Wikidata Timeline

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