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Buhmann, Martin Dietrich

Author ID: buhmann.martin-d Recent zbMATH articles by "Buhmann, Martin Dietrich"
Published as: Buhmann, M. D.; Buhmann, Martin D.; Buhmann, Martin; Buhmann, M.; Buhmann, M.d.
Homepage: https://www.uni-giessen.de/fbz/fb07/fachgebiete/mathematik/mathematik/ags/numeri...
External Links: MGP · ORCID · dblp · GND

Publications by Year

Citations contained in zbMATH Open

54 Publications have been cited 1,506 times in 1,199 Documents Cited by Year
Radial basis functions: theory and implementations. Zbl 1038.41001
Buhmann, M. D.
665
2003
Radial basis functions. Zbl 1004.65015
Buhmann, M. D.
185
2000
Multivariate cardinal interpolation with radial-basis functions. Zbl 0719.41007
Buhmann, M. D.
79
1990
Stability of the discretized pantograph differential equation. Zbl 0774.34057
Buhmann, Martin; Iserles, Arieh
70
1993
A new class of radial basis functions with compact support. Zbl 0956.41002
Buhmann, M. D.
50
2001
Spectral convergence of multiquadratic interpolation. Zbl 0791.41002
Buhmann, Martin; Dyn, Nira
45
1993
Convergence of univariate quasi-interpolation using multiquadrics. Zbl 0659.41003
Buhmann, M.d.
35
1988
On quasi-interpolation by radial basis functions with scattered centres. Zbl 0824.41010
Buhmann, M. D.; Dyn, N.; Levin, D.
35
1995
Multiquadratic interpolation improved. Zbl 0764.41001
Buhmann, Martin D.; Micchelli, Charles A.
28
1992
Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics. Zbl 0682.41007
Buhmann, M. D.
27
1990
On the dynamics of a discretized neutral equation. Zbl 0759.65056
Buhmann, M. D.; Iserles, A.
21
1992
Identifying linear combinations of ridge functions. Zbl 0931.41011
Buhmann, Martin D.; Pinkus, Allan
20
1999
On quasi-interpolation with radial basis functions. Zbl 0820.41006
Buhmann, M. D.
19
1993
Runge-Kutta methods for neutral differential equations. Zbl 0834.65061
Buhmann, M. D.; Iserles, A.; Nørsett, S. P.
17
1993
Radial functions on compact support. Zbl 0891.41005
Buhmann, M. D.
16
1998
Pointwise approximation with quasi-interpolation by radial basis functions. Zbl 1312.41005
Buhmann, Martin D.; Dai, Feng
14
2015
Radial basis function interpolation on an infinite regular grid. Zbl 0749.41002
Buhmann, M. D.; Powell, M. J. D.
13
1990
On orthogonal polynomials transformed by the QR algorithm. Zbl 0764.65008
Buhmann, M. D.; Iserles, A.
13
1992
Cardinal interpolation with radial basis functions: An integral transform approach. Zbl 0682.41006
Buhmann, M. D.
13
1989
Radial basis functions: theory and implementations. Reprint of the 2003 hardback ed. Zbl 1156.41001
Buhmann, M. D.
11
2009
Spline prewavelets for non-uniform knots. Zbl 0735.41009
Buhmann, Martin D.; Micchelli, Charles 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.
9
1995
Using two-slanted matrices for subdivision. Zbl 0802.65003
Buhmann, Martin D.; Micchelli, Charles A.
8
1994
A note on radial basis function interpolant limits. Zbl 1201.65017
Buhmann, Martin D.; Dinew, Slawomir; Larsson, Elisabeth
8
2010
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
Numerical analysis of functional equations with a variable delay. Zbl 0795.65048
Buhmann, M.; Iserles, A.
6
1992
Quasi-interpolation. Zbl 07468753
Buhmann, Martin; Jäger, Janin
6
2022
Discrete least squares approximation and prewavelets from radial function spaces. Zbl 0790.41015
Buhmann, M. D.
5
1993
Analysis of a new class of rational RBF expansions. Zbl 1465.65014
Buhmann, Martin D.; De Marchi, Stefano; Perracchione, Emma
5
2020
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.
4
2001
Radial basis functions: \(L^ p\)-approximation orders with scattered centres. Zbl 0824.41022
Buhmann, Martin D.; Ron, Amos
4
1994
Implementing and modifying Broyden class updates for large scale optimization. Zbl 1468.90125
Buhmann, Martin; Siegel, Dirk
4
2021
A note on the local stability of translates of radial basis functions. Zbl 0781.41018
Buhmann, M. D.; Chui, C. K.
3
1993
Knot removal with radial function interpolation. Zbl 0839.65003
Buhmann, Martin D.; Le Méhauté, Alain
3
1995
Pólya-type criteria for conditional strict positive definiteness of functions on spheres. Zbl 1446.41001
Buhmann, Martin; Jäger, Janin
3
2020
Compression using quasi-interpolation. Zbl 1381.41006
Buhmann, Martin D.; Dai, Feng
2
2015
Box spline prewavelets of small support. Zbl 1027.42032
Buhmann, M. D.; Davydov, O.; Goodman, T. N. T.
2
2001
Limits of radial basis function interpolants. Zbl 1160.41001
Buhmann, Martin D.; Dinew, Sławomir
2
2007
Completely monotonic functions for cardinal interpolation. Zbl 0705.41003
Buhmann, M. D.; Micchelli, C. A.
2
1989
Semi-infinite cardinal interpolation with multiquadrics and beyond. Zbl 1101.65010
Buhmann, M. D.
2
2006
Spectral properties and knot removal for interpolation by pure radial sums. Zbl 0835.65005
Buhmann, M. D.; Derrien, F.; Le Méhauté, A.
2
1995
On the convergence of cardinal interpolation by parameterized radial basis functions. Zbl 1367.41001
Buhmann, Martin D.; Feng, Han
2
2017
Topics in multivariate approximation and interpolation. Zbl 1205.41002
2
2006
Strict positive definiteness of convolutional and axially symmetric kernels on \(d\)-dimensional spheres. Zbl 1494.43003
Buhmann, Martin; Jäger, Janin
2
2022
Multiply monotone functions for radial basis function interpolation: extensions and new kernels. Zbl 1441.41001
Buhmann, Martin; Jäger, Janin
2
2020
Special issue: Radial basis functions and their applications. Zbl 0936.00009
1
1999
Pre-wavelets on scattered knots and from radial function spaces: A review. Zbl 0871.42025
Buhmann, M. D.
1
1996
M. J. D. Powell’s contributions to Numerical Mathematics. Zbl 1040.01512
Buhmann, Martin D.; Fletcher, Roger
1
1997
Asymptotically optimal approximation and numerical solutions of differential equations. Zbl 1031.65024
Buhmann, Martin D.; Micchelli, Charles A.; Ron, Amos
1
1997
Cubic spline prewavelets on the four-directional mesh. Zbl 1050.41009
Buhmann, M. D.; Davydov, O.; Goodman, T. N. T.
1
2003
Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure. Zbl 1517.43004
Buhmann, Martin; Jäger, Janin
1
2022
Quasi-interpolation. Zbl 07468753
Buhmann, Martin; Jäger, Janin
6
2022
Strict positive definiteness of convolutional and axially symmetric kernels on \(d\)-dimensional spheres. Zbl 1494.43003
Buhmann, Martin; Jäger, Janin
2
2022
Strictly positive definite kernels on the 2-sphere: from radial symmetry to eigenvalue block structure. Zbl 1517.43004
Buhmann, Martin; Jäger, Janin
1
2022
Implementing and modifying Broyden class updates for large scale optimization. Zbl 1468.90125
Buhmann, Martin; Siegel, Dirk
4
2021
Analysis of a new class of rational RBF expansions. Zbl 1465.65014
Buhmann, Martin D.; De Marchi, Stefano; Perracchione, Emma
5
2020
Pólya-type criteria for conditional strict positive definiteness of functions on spheres. Zbl 1446.41001
Buhmann, Martin; Jäger, Janin
3
2020
Multiply monotone functions for radial basis function interpolation: extensions and new kernels. Zbl 1441.41001
Buhmann, Martin; Jäger, Janin
2
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
14
2015
Compression using quasi-interpolation. Zbl 1381.41006
Buhmann, Martin D.; Dai, Feng
2
2015
A note on radial basis function interpolant limits. Zbl 1201.65017
Buhmann, Martin D.; Dinew, Slawomir; Larsson, Elisabeth
8
2010
Radial basis functions: theory and implementations. Reprint of the 2003 hardback ed. Zbl 1156.41001
Buhmann, M. D.
11
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
2
2006
Radial basis functions: theory and implementations. Zbl 1038.41001
Buhmann, M. D.
665
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.
50
2001
Approximation and interpolation with radial functions. Zbl 0991.41002
Buhmann, M. D.
4
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.
185
2000
Identifying linear combinations of ridge functions. Zbl 0931.41011
Buhmann, Martin D.; Pinkus, Allan
20
1999
Special issue: Radial basis functions and their applications. Zbl 0936.00009
1
1999
Radial functions on compact support. Zbl 0891.41005
Buhmann, M. D.
16
1998
On a recovery problem. Zbl 0892.42016
Buhmann, Martin; Pinkus, Allan
6
1997
M. J. D. Powell’s contributions to Numerical Mathematics. Zbl 1040.01512
Buhmann, Martin D.; Fletcher, Roger
1
1997
Asymptotically optimal approximation and numerical solutions of differential equations. Zbl 1031.65024
Buhmann, Martin D.; Micchelli, Charles A.; Ron, Amos
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.
35
1995
Multiquadric prewavelets on nonequally spaced knots in one dimension. Zbl 0842.41009
Buhmann, M. D.
9
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
4
1994
Stability of the discretized pantograph differential equation. Zbl 0774.34057
Buhmann, Martin; Iserles, Arieh
70
1993
Spectral convergence of multiquadratic interpolation. Zbl 0791.41002
Buhmann, Martin; Dyn, Nira
45
1993
On quasi-interpolation with radial basis functions. Zbl 0820.41006
Buhmann, M. D.
19
1993
Runge-Kutta methods for neutral differential equations. Zbl 0834.65061
Buhmann, M. D.; Iserles, A.; Nørsett, S. P.
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.
28
1992
On the dynamics of a discretized neutral equation. Zbl 0759.65056
Buhmann, M. D.; Iserles, A.
21
1992
On orthogonal polynomials transformed by the QR algorithm. Zbl 0764.65008
Buhmann, M. D.; Iserles, A.
13
1992
Spline prewavelets for non-uniform knots. Zbl 0735.41009
Buhmann, Martin D.; Micchelli, Charles A.
10
1992
Numerical analysis of functional equations with a variable delay. Zbl 0795.65048
Buhmann, M.; Iserles, A.
6
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.
79
1990
Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics. Zbl 0682.41007
Buhmann, M. D.
27
1990
Radial basis function interpolation on an infinite regular grid. Zbl 0749.41002
Buhmann, M. D.; Powell, M. J. D.
13
1990
Cardinal interpolation with radial basis functions: An integral transform approach. Zbl 0682.41006
Buhmann, M. D.
13
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.
35
1988
all top 5

Cited by 1,646 Authors

37 Dehghan Takht Fooladi, Mehdi
24 Cavoretto, Roberto
23 Buhmann, Martin Dietrich
21 De Rossi, Alessandra
20 Assari, Pouria
16 Ling, Leevan
16 Schaback, Robert
16 Wu, Zongmin
15 Chen, Ching-Shyang
15 Šarler, Božidar
14 Boyd, John Philip
13 Gao, Wenwu
13 Giesl, Peter
13 Kansa, Edward J.
13 Loeffler, Carlos Friedrich
12 Avazzadeh, Zakieh
12 Rad, Jamal Amani
12 Rossini, Milvia
11 Esmaeilbeigi, Mohsen
11 Fasshauer, Gregory E.
11 Rozza, Gianluigi
10 Davydov, Oleg V.
10 Fornberg, Bengt
10 Jung, Jae-Hun
10 Karageorghis, Andreas
10 Marcellán Español, Francisco
10 Perracchione, Emma
10 Sarra, Scott A.
9 Iske, Armin
9 Kazem, Saeed
9 Nikan, Omid
9 Siraj-ul-Islam
9 Sun, Zhengjie
9 Ye, Qi
8 Bozzini, Mira
8 Sezer, Mehmet
8 Wang, Wansheng
7 Adibi, Hojatollah
7 Baxter, Brad J. C.
7 Golbabai, Ahmad
7 Hon, Yiu-Chung
7 Ismailov, Vugar E.
7 Johnson, Michael James
7 Ledford, Jeff
7 Levesley, Jeremy
7 Mohammadi, Vahid
7 Ouazar, Driss
7 Wendland, Holger
7 Yoon, Jungho
6 Abbasbandy, Saeid
6 Bejancu, Aurelian jun.
6 De Marchi, Stefano
6 Dyn, Nira
6 Flyer, Natasha
6 Hamm, Keaton
6 Jäger, Janin
6 Luo, Zhen
6 Mansur, Webe Joao
6 Marrero, Isabel
6 Shoemaker, Christine A.
6 Yao, Guangming
5 Allasia, Giampietro
5 Bouhamidi, Abderrahman
5 Brunner, Hermann
5 Cao, Feilong
5 Chatrabgoun, Omid
5 de Melo Barcelos, Hercules
5 Driscoll, Tobin A.
5 Dubuc, Serge
5 Ferreira, António Joaquim Mendes
5 Hubbert, Simon
5 Kassab, Alain J.
5 Larsson, Elisabeth
5 Levin, David N.
5 Machado, José António Tenreiro
5 Maiorov, Vitaly Evgen’evich
5 Manzoni, Andrea
5 Micchelli, Charles A.
5 Oanh, Dang Thi
5 Parand, Kourosh
5 Platte, Rodrigo B.
5 Porcu, Emilio
5 Power, Henry
5 Quarteroni, Alfio M.
5 Shanazari, Kamal
5 Shivanian, Elyas
5 Sommariva, Alvise
5 Tatari, Mehdi
5 Uddin, Marjan
5 Vianello, Marco
5 Ward, Joseph Dinneen
5 Zhou, Xuan
4 Abbaszadeh, Mostafa
4 Aliev, Rashid Avazaga
4 Allen, Christian B.
4 Arteaga, Cristian
4 Bandler, John W.
4 Banei, Siamak
4 Barba, Lorena A.
4 Benkhaldoun, Fayssal
...and 1,546 more Authors
all top 5

Cited in 231 Serials

117 Engineering Analysis with Boundary Elements
70 Applied Mathematics and Computation
65 Computers & Mathematics with Applications
57 Journal of Computational and Applied Mathematics
53 Journal of Computational Physics
41 Journal of Approximation Theory
39 Applied Numerical Mathematics
37 Advances in Computational Mathematics
29 Computer Methods in Applied Mechanics and Engineering
28 Journal of Scientific Computing
26 Numerical Algorithms
25 Constructive Approximation
19 Applied Mathematical Modelling
19 International Journal of Computer Mathematics
18 SIAM Journal on Scientific Computing
15 Journal of Mathematical Analysis and Applications
15 International Journal for Numerical Methods in Engineering
15 Computational and Applied Mathematics
14 Mathematics and Computers in Simulation
13 Numerical Methods for Partial Differential Equations
11 Mathematics of Computation
10 Applied and Computational Harmonic Analysis
9 Journal of Global Optimization
8 Computers and Fluids
8 BIT
8 SIAM Journal on Numerical Analysis
8 International Journal of Computational Methods
7 Numerische Mathematik
7 Mathematical Problems in Engineering
6 Computer Physics Communications
6 International Journal for Numerical Methods in Fluids
6 Journal of Mathematical Sciences (New York)
6 Communications in Nonlinear Science and Numerical Simulation
6 Computational Methods for Differential Equations
6 International Journal of Applied and Computational Mathematics
5 Numerical Functional Analysis and Optimization
5 Computational Mechanics
5 Mathematical and Computer Modelling
5 Linear Algebra and its Applications
5 Inverse Problems in Science and Engineering
5 Mathematical Sciences
5 SIAM/ASA Journal on Uncertainty Quantification
4 Mathematical Methods in the Applied Sciences
4 Calcolo
4 Proceedings of the Edinburgh Mathematical Society. Series II
4 Neural Networks
4 Neural Computation
4 The Journal of Fourier Analysis and Applications
4 Optimization and Engineering
4 Journal of Applied Mathematics
4 Analysis and Applications (Singapore)
4 Acta Numerica
4 Proceedings of the Steklov Institute of Mathematics
3 Acta Mechanica
3 Journal of the Franklin Institute
3 Biometrics
3 Journal of Functional Analysis
3 Journal of Optimization Theory and Applications
3 Advances in Applied Mathematics
3 Journal of Complexity
3 Applied Mathematics Letters
3 SIAM Journal on Mathematical Analysis
3 Cybernetics and Systems Analysis
3 St. Petersburg Mathematical Journal
3 International Journal of Computational Fluid Dynamics
3 International Journal of Numerical Modelling
3 Acta Mathematica Sinica. English Series
3 International Journal of Nonlinear Sciences and Numerical Simulation
3 Foundations of Computational Mathematics
3 Discrete and Continuous Dynamical Systems. Series B
3 Mediterranean Journal of Mathematics
3 Advances in Difference Equations
3 Advances in Applied Mathematics and Mechanics
3 Journal of Computational Dynamics
2 Journal of Mathematical Physics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Wave Motion
2 Advances in Mathematics
2 Journal of Multivariate Analysis
2 Meccanica
2 Acta Mathematica Hungarica
2 Computer Aided Geometric Design
2 Acta Mathematicae Applicatae Sinica. English Series
2 European Journal of Operational Research
2 Computational Statistics and Data Analysis
2 Journal of Mathematical Imaging and Vision
2 Computational Optimization and Applications
2 Applied Mathematics. Series B (English Edition)
2 International Journal of Numerical Methods for Heat & Fluid Flow
2 Turkish Journal of Mathematics
2 Journal of Difference Equations and Applications
2 Abstract and Applied Analysis
2 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
2 Journal of Applied Statistics
2 Computational Geosciences
2 Archives of Computational Methods in Engineering
2 Sampling Theory in Signal and Image Processing
2 International Journal of Numerical Analysis and Modeling
2 Applications and Applied Mathematics
2 Optimization Letters
...and 131 more Serials
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Cited in 47 Fields

810 Numerical analysis (65-XX)
312 Approximations and expansions (41-XX)
187 Partial differential equations (35-XX)
104 Fluid mechanics (76-XX)
84 Mechanics of deformable solids (74-XX)
82 Harmonic analysis on Euclidean spaces (42-XX)
73 Ordinary differential equations (34-XX)
60 Statistics (62-XX)
56 Integral equations (45-XX)
45 Computer science (68-XX)
42 Operations research, mathematical programming (90-XX)
32 Functional analysis (46-XX)
27 Biology and other natural sciences (92-XX)
26 Real functions (26-XX)
25 Information and communication theory, circuits (94-XX)
24 Calculus of variations and optimal control; optimization (49-XX)
24 Classical thermodynamics, heat transfer (80-XX)
21 Probability theory and stochastic processes (60-XX)
20 Special functions (33-XX)
16 Linear and multilinear algebra; matrix theory (15-XX)
16 Dynamical systems and ergodic theory (37-XX)
15 Operator theory (47-XX)
15 Geophysics (86-XX)
15 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
14 Optics, electromagnetic theory (78-XX)
14 Systems theory; control (93-XX)
13 Difference and functional equations (39-XX)
11 Statistical mechanics, structure of matter (82-XX)
10 Potential theory (31-XX)
10 Abstract harmonic analysis (43-XX)
6 Convex and discrete geometry (52-XX)
6 Quantum theory (81-XX)
5 Functions of a complex variable (30-XX)
4 Integral transforms, operational calculus (44-XX)
4 Global analysis, analysis on manifolds (58-XX)
3 Combinatorics (05-XX)
2 Number theory (11-XX)
2 Astronomy and astrophysics (85-XX)
1 General and overarching topics; collections (00-XX)
1 History and biography (01-XX)
1 Commutative algebra (13-XX)
1 Nonassociative rings and algebras (17-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Algebraic topology (55-XX)
1 Mechanics of particles and systems (70-XX)

Citations by Year