×

zbMATH — the first resource for mathematics

Buhmann, Martin Dietrich

Compute Distance To:
Author ID: buhmann.martin-d Recent zbMATH articles by "Buhmann, Martin Dietrich"
Published as: Buhmann, M.; Buhmann, M. D.; Buhmann, M.d.; Buhmann, Martin; Buhmann, Martin D.
Homepage: https://www.uni-giessen.de/fbz/fb07/fachgebiete/mathematik/mathematik/ags/numeri...
External Links: MGP · ORCID · dblp · GND
Documents Indexed: 67 Publications since 1988, including 8 Books
Reviewing Activity: 539 Reviews

Publications by Year

Citations contained in zbMATH Open

49 Publications have been cited 1,231 times in 926 Documents Cited by Year
Radial basis functions: theory and implementations. Zbl 1038.41001
Buhmann, M. D.
520
2003
Radial basis functions. Zbl 1004.65015
Buhmann, M. D.
152
2000
Multivariate cardinal interpolation with radial-basis functions. Zbl 0719.41007
Buhmann, M. D.
68
1990
Stability of the discretized pantograph differential equation. Zbl 0774.34057
Buhmann, Martin; Iserles, Arieh
58
1993
A new class of radial basis functions with compact support. Zbl 0956.41002
Buhmann, M. D.
45
2001
Spectral convergence of multiquadratic interpolation. Zbl 0791.41002
Buhmann, Martin; Dyn, Nira
36
1993
Convergence of univariate quasi-interpolation using multiquadrics. Zbl 0659.41003
Buhmann, M.d.
31
1988
On quasi-interpolation by radial basis functions with scattered centres. Zbl 0824.41010
Buhmann, M. D.; Dyn, N.; Levin, D.
29
1995
Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics. Zbl 0682.41007
Buhmann, M. D.
26
1990
Multiquadratic interpolation improved. Zbl 0764.41001
Buhmann, Martin D.; Micchelli, Charles A.
25
1992
On the dynamics of a discretized neutral equation. Zbl 0759.65056
Buhmann, M. D.; Iserles, A.
19
1992
Runge-Kutta methods for neutral differential equations. Zbl 0834.65061
Buhmann, M. D.; Iserles, A.; Nørsett, S. P.
17
1993
On quasi-interpolation with radial basis functions. Zbl 0820.41006
Buhmann, M. D.
17
1993
Cardinal interpolation with radial basis functions: An integral transform approach. Zbl 0682.41006
Buhmann, M. D.
16
1989
Identifying linear combinations of ridge functions. Zbl 0931.41011
Buhmann, Martin D.; Pinkus, Allan
15
1999
Radial basis function interpolation on an infinite regular grid. Zbl 0749.41002
Buhmann, M. D.; Powell, M. J. D.
14
1990
Radial functions on compact support. Zbl 0891.41005
Buhmann, M. D.
13
1998
Pointwise approximation with quasi-interpolation by radial basis functions. Zbl 1312.41005
Buhmann, Martin D.; Dai, Feng
10
2015
On orthogonal polynomials transformed by the QR algorithm. Zbl 0764.65008
Buhmann, M. D.; Iserles, A.
10
1992
Multiply monotone functions for cardinal interpolation. Zbl 0756.41002
Buhmann, Martin D.; Micchelli, Charles A.
9
1991
Multiquadric prewavelets on nonequally spaced knots in one dimension. Zbl 0842.41009
Buhmann, M. D.
8
1995
Using two-slanted matrices for subdivision. Zbl 0802.65003
Buhmann, Martin D.; Micchelli, Charles A.
8
1994
Spline prewavelets for non-uniform knots. Zbl 0735.41009
Buhmann, Martin D.; Micchelli, Charles A.
8
1992
A note on radial basis function interpolant limits. Zbl 1201.65017
Buhmann, Martin D.; Dinew, Slawomir; Larsson, Elisabeth
7
2010
Numerical analysis of functional equations with a variable delay. Zbl 0795.65048
Buhmann, M.; Iserles, A.
7
1992
Error estimates for multiquadric interpolation. Zbl 0734.41003
Buhmann, M. D.; Dyn, N.
7
1991
On a recovery problem. Zbl 0892.42016
Buhmann, Martin; Pinkus, Allan
6
1997
Radial basis functions: theory and implementations. Reprint of the 2003 hardback ed. Zbl 1156.41001
Buhmann, M. D.
5
2009
Radial basis functions: \(L^ p\)-approximation orders with scattered centres. Zbl 0824.41022
Buhmann, Martin D.; Ron, Amos
5
1994
Discrete least squares approximation and prewavelets from radial function spaces. Zbl 0790.41015
Buhmann, M. D.
5
1993
On radial basis approximation on periodic grids. Zbl 0813.41003
Buhmann, Martin D.; Micchelli, Charles A.
4
1992
Approximation and interpolation with radial functions. Zbl 0991.41002
Buhmann, M. D.
3
2001
Knot removal with radial function interpolation. Zbl 0839.65003
Buhmann, Martin D.; Le Méhauté, Alain
3
1995
A note on the local stability of translates of radial basis functions. Zbl 0781.41018
Buhmann, M. D.; Chui, C. K.
3
1993
On the convergence of cardinal interpolation by parameterized radial basis functions. Zbl 1367.41001
Buhmann, Martin D.; Feng, Han
2
2017
Limits of radial basis function interpolants. Zbl 1160.41001
Buhmann, Martin D.; Dinew, Sławomir
2
2007
Semi-infinite cardinal interpolation with multiquadrics and beyond. Zbl 1101.65010
Buhmann, M. D.
2
2006
Box spline prewavelets of small support. Zbl 1027.42032
Buhmann, M. D.; Davydov, O.; Goodman, T. N. T.
2
2001
Special issue: Radial basis functions and their applications. Zbl 0936.00009
Buhmann, Martin (ed.)
2
1999
Spectral properties and knot removal for interpolation by pure radial sums. Zbl 0835.65005
Buhmann, M. D.; Derrien, F.; Le Méhauté, A.
2
1995
Completely monotonic functions for cardinal interpolation. Zbl 0705.41003
Buhmann, M. D.; Micchelli, C. A.
2
1989
Pólya-type criteria for conditional strict positive definiteness of functions on spheres. Zbl 1446.41001
Buhmann, Martin; Jäger, Janin
1
2020
Multiply monotone functions for radial basis function interpolation: extensions and new kernels. Zbl 1441.41001
Buhmann, Martin; Jäger, Janin
1
2020
Compression using quasi-interpolation. Zbl 1381.41006
Buhmann, Martin D.; Dai, Feng
1
2015
Topics in multivariate approximation and interpolation. Zbl 1205.41002
Jetter, Kurt (ed.); Buhmann, Martin (ed.); Haussmann, Werner (ed.); Schaback, Robert (ed.); Stoeckler, Joachim (ed.)
1
2006
Cubic spline prewavelets on the four-directional mesh. Zbl 1050.41009
Buhmann, M. D.; Davydov, O.; Goodman, T. N. T.
1
2003
Asymptotically optimal approximation and numerical solutions of differential equations. Zbl 1031.65024
Buhmann, Martin D.; Micchelli, Charles A.; Ron, Amos
1
1997
M. J. D. Powell’s contributions to Numerical Mathematics. Zbl 1040.01512
Buhmann, Martin D.; Fletcher, Roger
1
1997
Pre-wavelets on scattered knots and from radial function spaces: A review. Zbl 0871.42025
Buhmann, M. D.
1
1996
Pólya-type criteria for conditional strict positive definiteness of functions on spheres. Zbl 1446.41001
Buhmann, Martin; Jäger, Janin
1
2020
Multiply monotone functions for radial basis function interpolation: extensions and new kernels. Zbl 1441.41001
Buhmann, Martin; Jäger, Janin
1
2020
On the convergence of cardinal interpolation by parameterized radial basis functions. Zbl 1367.41001
Buhmann, Martin D.; Feng, Han
2
2017
Pointwise approximation with quasi-interpolation by radial basis functions. Zbl 1312.41005
Buhmann, Martin D.; Dai, Feng
10
2015
Compression using quasi-interpolation. Zbl 1381.41006
Buhmann, Martin D.; Dai, Feng
1
2015
A note on radial basis function interpolant limits. Zbl 1201.65017
Buhmann, Martin D.; Dinew, Slawomir; Larsson, Elisabeth
7
2010
Radial basis functions: theory and implementations. Reprint of the 2003 hardback ed. Zbl 1156.41001
Buhmann, M. D.
5
2009
Limits of radial basis function interpolants. Zbl 1160.41001
Buhmann, Martin D.; Dinew, Sławomir
2
2007
Semi-infinite cardinal interpolation with multiquadrics and beyond. Zbl 1101.65010
Buhmann, M. D.
2
2006
Topics in multivariate approximation and interpolation. Zbl 1205.41002
Jetter, Kurt (ed.); Buhmann, Martin (ed.); Haussmann, Werner (ed.); Schaback, Robert (ed.); Stoeckler, Joachim (ed.)
1
2006
Radial basis functions: theory and implementations. Zbl 1038.41001
Buhmann, M. D.
520
2003
Cubic spline prewavelets on the four-directional mesh. Zbl 1050.41009
Buhmann, M. D.; Davydov, O.; Goodman, T. N. T.
1
2003
A new class of radial basis functions with compact support. Zbl 0956.41002
Buhmann, M. D.
45
2001
Approximation and interpolation with radial functions. Zbl 0991.41002
Buhmann, M. D.
3
2001
Box spline prewavelets of small support. Zbl 1027.42032
Buhmann, M. D.; Davydov, O.; Goodman, T. N. T.
2
2001
Radial basis functions. Zbl 1004.65015
Buhmann, M. D.
152
2000
Identifying linear combinations of ridge functions. Zbl 0931.41011
Buhmann, Martin D.; Pinkus, Allan
15
1999
Special issue: Radial basis functions and their applications. Zbl 0936.00009
Buhmann, Martin (ed.)
2
1999
Radial functions on compact support. Zbl 0891.41005
Buhmann, M. D.
13
1998
On a recovery problem. Zbl 0892.42016
Buhmann, Martin; Pinkus, Allan
6
1997
Asymptotically optimal approximation and numerical solutions of differential equations. Zbl 1031.65024
Buhmann, Martin D.; Micchelli, Charles A.; Ron, Amos
1
1997
M. J. D. Powell’s contributions to Numerical Mathematics. Zbl 1040.01512
Buhmann, Martin D.; Fletcher, Roger
1
1997
Pre-wavelets on scattered knots and from radial function spaces: A review. Zbl 0871.42025
Buhmann, M. D.
1
1996
On quasi-interpolation by radial basis functions with scattered centres. Zbl 0824.41010
Buhmann, M. D.; Dyn, N.; Levin, D.
29
1995
Multiquadric prewavelets on nonequally spaced knots in one dimension. Zbl 0842.41009
Buhmann, M. D.
8
1995
Knot removal with radial function interpolation. Zbl 0839.65003
Buhmann, Martin D.; Le Méhauté, Alain
3
1995
Spectral properties and knot removal for interpolation by pure radial sums. Zbl 0835.65005
Buhmann, M. D.; Derrien, F.; Le Méhauté, A.
2
1995
Using two-slanted matrices for subdivision. Zbl 0802.65003
Buhmann, Martin D.; Micchelli, Charles A.
8
1994
Radial basis functions: \(L^ p\)-approximation orders with scattered centres. Zbl 0824.41022
Buhmann, Martin D.; Ron, Amos
5
1994
Stability of the discretized pantograph differential equation. Zbl 0774.34057
Buhmann, Martin; Iserles, Arieh
58
1993
Spectral convergence of multiquadratic interpolation. Zbl 0791.41002
Buhmann, Martin; Dyn, Nira
36
1993
Runge-Kutta methods for neutral differential equations. Zbl 0834.65061
Buhmann, M. D.; Iserles, A.; Nørsett, S. P.
17
1993
On quasi-interpolation with radial basis functions. Zbl 0820.41006
Buhmann, M. D.
17
1993
Discrete least squares approximation and prewavelets from radial function spaces. Zbl 0790.41015
Buhmann, M. D.
5
1993
A note on the local stability of translates of radial basis functions. Zbl 0781.41018
Buhmann, M. D.; Chui, C. K.
3
1993
Multiquadratic interpolation improved. Zbl 0764.41001
Buhmann, Martin D.; Micchelli, Charles A.
25
1992
On the dynamics of a discretized neutral equation. Zbl 0759.65056
Buhmann, M. D.; Iserles, A.
19
1992
On orthogonal polynomials transformed by the QR algorithm. Zbl 0764.65008
Buhmann, M. D.; Iserles, A.
10
1992
Spline prewavelets for non-uniform knots. Zbl 0735.41009
Buhmann, Martin D.; Micchelli, Charles A.
8
1992
Numerical analysis of functional equations with a variable delay. Zbl 0795.65048
Buhmann, M.; Iserles, A.
7
1992
On radial basis approximation on periodic grids. Zbl 0813.41003
Buhmann, Martin D.; Micchelli, Charles A.
4
1992
Multiply monotone functions for cardinal interpolation. Zbl 0756.41002
Buhmann, Martin D.; Micchelli, Charles A.
9
1991
Error estimates for multiquadric interpolation. Zbl 0734.41003
Buhmann, M. D.; Dyn, N.
7
1991
Multivariate cardinal interpolation with radial-basis functions. Zbl 0719.41007
Buhmann, M. D.
68
1990
Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics. Zbl 0682.41007
Buhmann, M. D.
26
1990
Radial basis function interpolation on an infinite regular grid. Zbl 0749.41002
Buhmann, M. D.; Powell, M. J. D.
14
1990
Cardinal interpolation with radial basis functions: An integral transform approach. Zbl 0682.41006
Buhmann, M. D.
16
1989
Completely monotonic functions for cardinal interpolation. Zbl 0705.41003
Buhmann, M. D.; Micchelli, C. A.
2
1989
Convergence of univariate quasi-interpolation using multiquadrics. Zbl 0659.41003
Buhmann, M.d.
31
1988
all top 5

Cited by 1,306 Authors

26 Dehghan Takht Fooladi, Mehdi
22 Buhmann, Martin Dietrich
21 Wu, Zongmin
18 Cavoretto, Roberto
17 De Rossi, Alessandra
15 Boyd, John Philip
14 Ling, Leevan
14 Šarler, Božidar
13 Assari, Pouria
13 Chen, Ching-Shyang
13 Kansa, Edward J.
12 Schaback, Robert
11 Rad, Jamal Amani
10 Fornberg, Bengt
10 Gao, Wenwu
10 Rossini, Milvia
10 Sarra, Scott A.
9 Esmaeilbeigi, Mohsen
9 Karageorghis, Andreas
9 Loeffler, Carlos Friedrich
9 Perracchione, Emma
9 Ye, Qi
8 Fasshauer, Gregory E.
8 Giesl, Peter
8 Jung, Jae-Hun
8 Kazem, Saeed
8 Marcellán Español, Francisco
8 Parand, Kourosh
7 Bozzini, Mira
7 Davydov, Oleg V.
7 Iske, Armin
7 Johnson, Michael James
7 Sezer, Mehmet
7 Siraj-ul-Islam
6 Adibi, Hojatollah
6 Avazzadeh, Zakieh
6 Baxter, Brad J. C.
6 Dyn, Nira
6 Flyer, Natasha
6 Hamm, Keaton
6 Hon, Yiu-Chung
6 Ledford, Jeff
6 Levesley, Jeremy
6 Marrero, Isabel
6 Mohammadi, Vahid
6 Wang, Wansheng
6 Yoon, Jungho
5 Abbasbandy, Saeid
5 Allasia, Giampietro
5 Bouhamidi, Abderrahman
5 Brunner, Hermann
5 Cao, Feilong
5 Chatrabgoun, Omid
5 De Marchi, Stefano
5 Driscoll, Tobin A.
5 Dubuc, Serge
5 Ferreira, António Joaquim Mendes
5 Golbabai, Ahmad
5 Ismailov, Vugar E.
5 Larsson, Elisabeth
5 Luo, Zhen
5 Maiorov, Vitaly Evgen’evich
5 Manzoni, Andrea
5 Micchelli, Charles A.
5 Platte, Rodrigo B.
5 Power, Henry
5 Quarteroni, Alfio M.
5 Shoemaker, Christine A.
5 Sun, Zhengjie
5 Tatari, Mehdi
5 Wang, Renhong
5 Ward, Joseph Dinneen
5 Wendland, Holger
5 Yao, Guangming
5 Zhang, Yunxin
5 Zhou, Xuan
4 Allen, Christian B.
4 Arteaga, Cristian
4 Barba, Lorena A.
4 Bejancu, Aurelian jun.
4 Chui, Charles Kam-tai
4 Djidjeli, K.
4 Hangelbroek, Thomas C.
4 Hickernell, Fred J.
4 Jakobsson, Stefan
4 Kassab, Alain J.
4 Kounchev, Ognyan Ivanov
4 Lenarduzzi, Licia
4 Li, Jichun
4 Liu, Mingzhu
4 Liu, Xiaoyan
4 Ma, Limin
4 Mansur, Webe Joao
4 Parand, Koroush
4 Popov, Viktor
4 Porcu, Emilio
4 Regis, Rommel G.
4 Rendall, Thomas C. S.
4 Render, Hermann
4 Roque, C. M. C.
...and 1,206 more Authors
all top 5

Cited in 178 Serials

103 Engineering Analysis with Boundary Elements
65 Applied Mathematics and Computation
62 Computers & Mathematics with Applications
48 Journal of Computational and Applied Mathematics
43 Journal of Computational Physics
38 Journal of Approximation Theory
32 Applied Numerical Mathematics
28 Advances in Computational Mathematics
21 Constructive Approximation
21 Journal of Scientific Computing
21 Numerical Algorithms
15 SIAM Journal on Scientific Computing
14 Computer Methods in Applied Mechanics and Engineering
14 Applied Mathematical Modelling
12 Numerical Methods for Partial Differential Equations
11 Journal of Mathematical Analysis and Applications
11 Mathematics of Computation
11 International Journal for Numerical Methods in Engineering
11 International Journal of Computer Mathematics
10 Computational and Applied Mathematics
8 Computers and Fluids
8 Journal of Global Optimization
8 International Journal of Computational Methods
7 BIT
7 Mathematics and Computers in Simulation
7 Mathematical Problems in Engineering
6 International Journal for Numerical Methods in Fluids
6 Numerische Mathematik
6 SIAM Journal on Numerical Analysis
6 Applied and Computational Harmonic Analysis
5 Computational Mechanics
5 Mathematical and Computer Modelling
5 Linear Algebra and its Applications
5 Journal of Mathematical Sciences (New York)
5 Inverse Problems in Science and Engineering
5 SIAM/ASA Journal on Uncertainty Quantification
4 Computer Physics Communications
4 Numerical Functional Analysis and Optimization
4 Proceedings of the Edinburgh Mathematical Society. Series II
4 Journal of Applied Mathematics
4 Analysis and Applications (Singapore)
4 Mathematical Sciences
3 Acta Mechanica
3 Mathematical Methods in the Applied Sciences
3 Biometrics
3 Calcolo
3 Advances in Applied Mathematics
3 Neural Networks
3 Neural Computation
3 SIAM Journal on Mathematical Analysis
3 Cybernetics and Systems Analysis
3 International Journal of Numerical Modelling
3 Communications in Nonlinear Science and Numerical Simulation
3 Optimization and Engineering
3 Foundations of Computational Mathematics
3 Discrete and Continuous Dynamical Systems. Series B
2 Journal d’Analyse Mathématique
2 Journal of the Franklin Institute
2 Journal of Mathematical Physics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Advances in Mathematics
2 Journal of Functional Analysis
2 Meccanica
2 Computer Aided Geometric Design
2 Acta Mathematicae Applicatae Sinica. English Series
2 Journal of Complexity
2 Applied Mathematics Letters
2 European Journal of Operational Research
2 Computational Optimization and Applications
2 Applied Mathematics. Series B (English Edition)
2 St. Petersburg Mathematical Journal
2 International Journal of Numerical Methods for Heat & Fluid Flow
2 Journal of Difference Equations and Applications
2 The Journal of Fourier Analysis and Applications
2 Abstract and Applied Analysis
2 Acta Mathematica Sinica. English Series
2 Archives of Computational Methods in Engineering
2 Mediterranean Journal of Mathematics
2 Proceedings of the Steklov Institute of Mathematics
2 Science China. Mathematics
2 Afrika Matematika
2 International Journal of Applied and Computational Mathematics
1 Applicable Analysis
1 The Canadian Journal of Statistics
1 International Journal of Heat and Mass Transfer
1 Israel Journal of Mathematics
1 Mathematische Semesterberichte
1 Nonlinearity
1 Rocky Mountain Journal of Mathematics
1 Scandinavian Journal of Statistics
1 Wave Motion
1 Information Sciences
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of Multivariate Analysis
1 Journal of Optimization Theory and Applications
1 Memoirs of the American Mathematical Society
1 Ricerche di Matematica
1 Transactions of the American Mathematical Society
1 Zeitschrift für Analysis und ihre Anwendungen
1 Statistics & Probability Letters
...and 78 more Serials
all top 5

Cited in 45 Fields

624 Numerical analysis (65-XX)
258 Approximations and expansions (41-XX)
129 Partial differential equations (35-XX)
80 Fluid mechanics (76-XX)
63 Harmonic analysis on Euclidean spaces (42-XX)
63 Mechanics of deformable solids (74-XX)
58 Ordinary differential equations (34-XX)
44 Statistics (62-XX)
42 Integral equations (45-XX)
29 Computer science (68-XX)
28 Functional analysis (46-XX)
28 Operations research, mathematical programming (90-XX)
23 Classical thermodynamics, heat transfer (80-XX)
20 Information and communication theory, circuits (94-XX)
19 Real functions (26-XX)
17 Biology and other natural sciences (92-XX)
14 Probability theory and stochastic processes (60-XX)
13 Linear and multilinear algebra; matrix theory (15-XX)
13 Optics, electromagnetic theory (78-XX)
13 Geophysics (86-XX)
13 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
12 Difference and functional equations (39-XX)
12 Operator theory (47-XX)
12 Calculus of variations and optimal control; optimization (49-XX)
10 Special functions (33-XX)
10 Dynamical systems and ergodic theory (37-XX)
10 Statistical mechanics, structure of matter (82-XX)
7 Potential theory (31-XX)
7 Abstract harmonic analysis (43-XX)
6 Convex and discrete geometry (52-XX)
6 Systems theory; control (93-XX)
5 Functions of a complex variable (30-XX)
3 Quantum theory (81-XX)
2 Integral transforms, operational calculus (44-XX)
2 Global analysis, analysis on manifolds (58-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Combinatorics (05-XX)
1 Number theory (11-XX)
1 Commutative algebra (13-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Mechanics of particles and systems (70-XX)
1 Astronomy and astrophysics (85-XX)

Citations by Year