Compute Distance To:
 Documents Indexed: 84 Publications since 1974 Co-Authors: 29 Co-Authors with 32 Joint Publications 555 Co-Co-Authors
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### Co-Authors

 38 single-authored 6 Bailey, Barbara A. 4 Narcowich, Francis J. 3 Allen, G. Donald 3 Chui, Charles Kam-tai 3 Lorentz, Rudolph Alexander 3 Lyubarskii, Yurii I. 3 Smith, Philip W. 2 Crawford, Edward F. 2 Filbir, Frank-Dieter 2 Giné-Masdéu, Evarist 2 Larsen, Russell D. 1 Ansorg, Marcus 1 Dlin, F. 1 Fink, Arlington Michael 1 Gröchenig, Karlheinz 1 Güntürk, Cemalettin Sinan 1 Hangelbroek, Thomas C. 1 Hielscher, Ralf 1 Jordan, G. Samuel 1 Kaiblinger, Norbert 1 Kaßmann, Moritz 1 Potter, E. H. 1 Riviere, Nestor M. 1 Sahakyan, Artur A. 1 Seyfried, Ruben 1 Solmon, Donald C. 1 Szeptycki, Pawel 1 Ward, Joseph Dinneen 1 Wheeler, Robert Lee
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### Serials

 9 Journal of Approximation Theory 8 Proceedings of the American Mathematical Society 5 Applied and Computational Harmonic Analysis 3 Journal of Functional Analysis 3 Transactions of the American Mathematical Society 3 The Journal of Fourier Analysis and Applications 3 Sampling Theory in Signal and Image Processing 2 Bulletin of the Australian Mathematical Society 2 Houston Journal of Mathematics 2 Indiana University Mathematics Journal 2 SIAM Journal on Applied Mathematics 2 SIAM Journal on Mathematical Analysis 1 Applicable Analysis 1 Computers and Chemistry 1 Computers & Mathematics with Applications 1 IEEE Transactions on Information Theory 1 Inverse Problems 1 Journal d’Analyse Mathématique 1 Mathematical Methods in the Applied Sciences 1 Studia Mathematica 1 Mathematics of Computation 1 Statistics & Probability Letters 1 Approximation Theory and its Applications 1 Journal of Integral Equations and Applications 1 IEEE Transactions on Acoustics, Speech, and Signal Processing 1 Experimental Mathematics 1 Filomat 1 Jaen Journal on Approximation
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### Fields

 35 Approximations and expansions (41-XX) 29 Harmonic analysis on Euclidean spaces (42-XX) 16 Integral transforms, operational calculus (44-XX) 15 Numerical analysis (65-XX) 14 Information and communication theory, circuits (94-XX) 10 Functions of a complex variable (30-XX) 7 Sequences, series, summability (40-XX) 7 Functional analysis (46-XX) 6 Real functions (26-XX) 4 Integral equations (45-XX) 3 Statistics (62-XX) 3 Biology and other natural sciences (92-XX) 2 Potential theory (31-XX) 2 Partial differential equations (35-XX) 2 Abstract harmonic analysis (43-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Difference and functional equations (39-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Probability theory and stochastic processes (60-XX) 1 Computer science (68-XX) 1 Fluid mechanics (76-XX)

### Citations contained in zbMATH Open

65 Publications have been cited 1,015 times in 741 Documents Cited by Year
Multivariate interpolation and conditionally positive definite functions. II. Zbl 0859.41004
Madych, W. R.; Nelson, S. A.
1990
Multiresolution analysis, Haar bases, and self-similar tilings of $$R^ n$$. Zbl 0742.42012
1992
Miscellaneous error bounds for multiquadric and related interpolators. Zbl 0766.41003
1992
Multivariate interpolation and conditionally positive definite functions. Zbl 0703.41008
Madych, W. R.; Nelson, S. A.
1988
Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation. Zbl 0764.41003
Madych, W. R.; Nelson, S. A.
1992
Polyharmonic cardinal splines. Zbl 0702.41020
Madych, W. R.; Nelson, S. A.
1990
Some elementary properties of multiresolution analyses of $$L^ 2(R^ n)$$. Zbl 0760.41030
1992
The recovery of irregularly sampled band limited functions via tempered splines. Zbl 0873.41012
1994
An estimate for multivariate interpolation. II. Zbl 1119.41003
2006
On Littlewood-Paley functions. Zbl 0247.44005
1974
Cardinal interpolation with Gaussian kernels. Zbl 1247.41004
Hangelbroek, T.; Madych, W.; Narcowich, F.; Ward, J. D.
2012
An estimate for multivariate interpolation. Zbl 0558.41008
Madych, W. R.; Potter, E. H.
1985
Finite orthogonal transforms and multiresolution analyses on intervals. Zbl 0926.42022
1997
Error bounds for multiquadric interpolation. Zbl 0738.41007
Madych, W. R.; Nelson, S. A.
1989
Difference quotients and elliptic mixed boundary problems of second order. Zbl 1213.35201
2007
Padé approximation of Stieltjes series. Zbl 0323.30044
Allen, G. D.; Chui, C. K.; Madych, W. R.; Narcowich, F. J.; Smith, P. W.
1975
Translation and dilation invariant subspaces of $$L^2(\mathbb{R})$$ and multiresolution analyses. Zbl 0926.42020
Lorentz, R. A.; Madych, W. R.; Sahakian, A.
1998
Tomography, approximate reconstruction, and continuous wavelet transforms. Zbl 0945.42021
1999
Multipliers of the Hölder classes. Zbl 0338.46035
Madych, W. R.; Riviere, N. M.
1976
Spline type summability for multivariate sampling. Zbl 0943.94002
1999
Convergence of classical cardinal series and band limited special functions. Zbl 1315.40001
Bailey, B. A.; Madych, W. R.
2013
Polyharmonic splines, multiscale analysis, and entire functions. Zbl 0707.41012
1990
Polyharmonic cardinal splines: A minimization property. Zbl 0719.41016
Madych, W. R.; Nelson, S. A.
1990
Summability kernels for circular and spherical mean data. Zbl 1269.44001
Ansorg, Marcus; Filbir, Frank; Madych, W. R.; Seyfried, Ruben
2013
Summability of Lagrange type interpolation series. Zbl 0980.41019
2001
Convergence of classical cardinal series. Zbl 1338.40008
2013
Summability and approximate reconstruction from Radon transform data. Zbl 0748.65092
1991
Cardinal sine series, oversampling, and periodic distributions. Zbl 1329.30014
Bailey, B. A.; Madych, W. R.
2015
Classical sampling series of band limited functions: oversampling and non-existence. Zbl 1417.94029
Bailey, B. A.; Madych, W. R.
2016
Polynomial based algorithms for computed tomography. Zbl 0507.65045
Madych, W. R.; Nelson, S. A.
1983
Absolute summability of Fourier transforms on $$R^n$$. Zbl 0327.42008
1976
On the periodized square of $$L^2$$ cardinal splines. Zbl 1262.41007
Giné, E.; Güntürk, C. S.; Madych, W. R.
2011
Convergence and summability of cardinal sine series. Zbl 1423.30020
Bailey, B. A.; Madych, W. R.
2018
Orthogonal wavelet bases for $$L^ 2(\mathbb{R}^ n)$$. Zbl 0807.42023
1994
On wavelet projection kernels and the integrated squared error in density estimation. Zbl 1288.62057
2014
Interpolation of functions from generalized Paley–Wiener spaces. Zbl 1085.30023
2005
On certain bounded solutions of $$g^*\mu=f$$. Zbl 0431.45004
Fink, A. M.; Madych, W. R.
1979
Padé approximation and orthogonal polynomials. Zbl 0279.41014
Allen, G. D.; Chui, C. K.; Madych, W. R.; Narcowich, F. J.; Smith, P. W.
1974
Reconstruction from circular and spherical mean data. Zbl 1192.68767
Filbir, Frank; Hielscher, Ralf; Madych, W. R.
2010
On the correctness of the problem of inverting the finite Hilbert transform in certain aeroelastic models. Zbl 0701.44003
1990
A range theorem for the Radon transform. Zbl 0658.44003
Madych, W. R.; Solmon, D. C.
1988
Functions of exponential type and the cardinal series. Zbl 1293.30063
Bailey, B. A.; Madych, W. R.
2014
The limiting behavior of certain sampling series and cardinal splines. Zbl 1434.94044
2020
On the closure of the union of nested subspaces of $$L^2(\mathbb{R}^d)$$. Zbl 0936.42025
Lorentz, R. A.; Madych, W. R.
1998
Characterization of tomographic reconstructions which commute with rigid motions. Zbl 0511.65094
Madych, W. R.; Nelson, S. A.
1982
Polynomial based algorithms for computed tomography. II. Zbl 0534.65087
Madych, W. R.; Nelson, S. A.
1984
Irregular Poisson type summation. Zbl 1182.42010
2008
Allen, G. D.; Chui, C. K.; Madych, W. R.; Narcowich, F. J.; Smith, P. W.
1974
Iterated Littlewood-Paley functions and a multiplier theorem. Zbl 0292.42006
1974
Cardinal interpolation with polyharmonic splines. Zbl 0692.41003
1989
Cardinal sine series: convergence and uniqueness. Zbl 1346.94071
Bailey, B. A.; Madych, W. R.
2014
2004
Solutions of underdetermined systems of linear equations. Zbl 0769.65019
1991
On the convergence of cardinal splines. Zbl 1457.41003
2020
Error estimates for interpolation by generalized splines. Zbl 0735.41003
1991
Wavelets and generalized box splines. Zbl 0725.41009
Lorentz, R. A. H.; Madych, W. R.
1992
Linear convolution integral equations with asymptotically almost periodic solutions. Zbl 0445.45005
Jordan, G. S.; Madych, W. R.; Wheeler, R. L.
1980
Degree of approximation in computerized tomography. Zbl 0482.41014
1980
Orthonormal sampling functions. Zbl 1106.42022
2006
Approximate inversion formulas for Radon transform data. Zbl 0537.41021
Madych, W. R.; Nelson, S. A.
1983
Limits of dilated convolution transforms. Zbl 0572.42016
1985
Radial sums of ridge functions: a characterization. Zbl 0577.44004
Madych, W. R.; Nelson, S. A.
1985
Reconstruction from restricted Radon transform data: resolution and ill- conditionedness. Zbl 0627.44006
Madych, W. R.; Nelson, S. A.
1986
Anisotropic $$H^p$$, real interpolation, and fractional Riesz potentials. Zbl 0368.46038
1977
Distributions with strong maximal functions in $$L^p(R^n)$$. Zbl 0426.46027
1979
The limiting behavior of certain sampling series and cardinal splines. Zbl 1434.94044
2020
On the convergence of cardinal splines. Zbl 1457.41003
2020
Convergence and summability of cardinal sine series. Zbl 1423.30020
Bailey, B. A.; Madych, W. R.
2018
Classical sampling series of band limited functions: oversampling and non-existence. Zbl 1417.94029
Bailey, B. A.; Madych, W. R.
2016
Cardinal sine series, oversampling, and periodic distributions. Zbl 1329.30014
Bailey, B. A.; Madych, W. R.
2015
On wavelet projection kernels and the integrated squared error in density estimation. Zbl 1288.62057
2014
Functions of exponential type and the cardinal series. Zbl 1293.30063
Bailey, B. A.; Madych, W. R.
2014
Cardinal sine series: convergence and uniqueness. Zbl 1346.94071
Bailey, B. A.; Madych, W. R.
2014
Convergence of classical cardinal series and band limited special functions. Zbl 1315.40001
Bailey, B. A.; Madych, W. R.
2013
Summability kernels for circular and spherical mean data. Zbl 1269.44001
Ansorg, Marcus; Filbir, Frank; Madych, W. R.; Seyfried, Ruben
2013
Convergence of classical cardinal series. Zbl 1338.40008
2013
Cardinal interpolation with Gaussian kernels. Zbl 1247.41004
Hangelbroek, T.; Madych, W.; Narcowich, F.; Ward, J. D.
2012
On the periodized square of $$L^2$$ cardinal splines. Zbl 1262.41007
Giné, E.; Güntürk, C. S.; Madych, W. R.
2011
Reconstruction from circular and spherical mean data. Zbl 1192.68767
Filbir, Frank; Hielscher, Ralf; Madych, W. R.
2010
Irregular Poisson type summation. Zbl 1182.42010
2008
Difference quotients and elliptic mixed boundary problems of second order. Zbl 1213.35201
2007
An estimate for multivariate interpolation. II. Zbl 1119.41003
2006
Orthonormal sampling functions. Zbl 1106.42022
2006
Interpolation of functions from generalized Paley–Wiener spaces. Zbl 1085.30023
2005
2004
Summability of Lagrange type interpolation series. Zbl 0980.41019
2001
Tomography, approximate reconstruction, and continuous wavelet transforms. Zbl 0945.42021
1999
Spline type summability for multivariate sampling. Zbl 0943.94002
1999
Translation and dilation invariant subspaces of $$L^2(\mathbb{R})$$ and multiresolution analyses. Zbl 0926.42020
Lorentz, R. A.; Madych, W. R.; Sahakian, A.
1998
On the closure of the union of nested subspaces of $$L^2(\mathbb{R}^d)$$. Zbl 0936.42025
Lorentz, R. A.; Madych, W. R.
1998
Finite orthogonal transforms and multiresolution analyses on intervals. Zbl 0926.42022
1997
The recovery of irregularly sampled band limited functions via tempered splines. Zbl 0873.41012
1994
Orthogonal wavelet bases for $$L^ 2(\mathbb{R}^ n)$$. Zbl 0807.42023
1994
Multiresolution analysis, Haar bases, and self-similar tilings of $$R^ n$$. Zbl 0742.42012
1992
Miscellaneous error bounds for multiquadric and related interpolators. Zbl 0766.41003
1992
Bounds on multivariate polynomials and exponential error estimates for multiquadric interpolation. Zbl 0764.41003
Madych, W. R.; Nelson, S. A.
1992
Some elementary properties of multiresolution analyses of $$L^ 2(R^ n)$$. Zbl 0760.41030
1992
Wavelets and generalized box splines. Zbl 0725.41009
Lorentz, R. A. H.; Madych, W. R.
1992
Summability and approximate reconstruction from Radon transform data. Zbl 0748.65092
1991
Solutions of underdetermined systems of linear equations. Zbl 0769.65019
1991
Error estimates for interpolation by generalized splines. Zbl 0735.41003
1991
Multivariate interpolation and conditionally positive definite functions. II. Zbl 0859.41004
Madych, W. R.; Nelson, S. A.
1990
Polyharmonic cardinal splines. Zbl 0702.41020
Madych, W. R.; Nelson, S. A.
1990
Polyharmonic splines, multiscale analysis, and entire functions. Zbl 0707.41012
1990
Polyharmonic cardinal splines: A minimization property. Zbl 0719.41016
Madych, W. R.; Nelson, S. A.
1990
On the correctness of the problem of inverting the finite Hilbert transform in certain aeroelastic models. Zbl 0701.44003
1990
Error bounds for multiquadric interpolation. Zbl 0738.41007
Madych, W. R.; Nelson, S. A.
1989
Cardinal interpolation with polyharmonic splines. Zbl 0692.41003
1989
Multivariate interpolation and conditionally positive definite functions. Zbl 0703.41008
Madych, W. R.; Nelson, S. A.
1988
A range theorem for the Radon transform. Zbl 0658.44003
Madych, W. R.; Solmon, D. C.
1988
Reconstruction from restricted Radon transform data: resolution and ill- conditionedness. Zbl 0627.44006
Madych, W. R.; Nelson, S. A.
1986
An estimate for multivariate interpolation. Zbl 0558.41008
Madych, W. R.; Potter, E. H.
1985
Limits of dilated convolution transforms. Zbl 0572.42016
1985
Radial sums of ridge functions: a characterization. Zbl 0577.44004
Madych, W. R.; Nelson, S. A.
1985
Polynomial based algorithms for computed tomography. II. Zbl 0534.65087
Madych, W. R.; Nelson, S. A.
1984
Polynomial based algorithms for computed tomography. Zbl 0507.65045
Madych, W. R.; Nelson, S. A.
1983
Approximate inversion formulas for Radon transform data. Zbl 0537.41021
Madych, W. R.; Nelson, S. A.
1983
Characterization of tomographic reconstructions which commute with rigid motions. Zbl 0511.65094
Madych, W. R.; Nelson, S. A.
1982
Linear convolution integral equations with asymptotically almost periodic solutions. Zbl 0445.45005
Jordan, G. S.; Madych, W. R.; Wheeler, R. L.
1980
Degree of approximation in computerized tomography. Zbl 0482.41014
1980
On certain bounded solutions of $$g^*\mu=f$$. Zbl 0431.45004
Fink, A. M.; Madych, W. R.
1979
Distributions with strong maximal functions in $$L^p(R^n)$$. Zbl 0426.46027
1979
Anisotropic $$H^p$$, real interpolation, and fractional Riesz potentials. Zbl 0368.46038
1977
Multipliers of the Hölder classes. Zbl 0338.46035
Madych, W. R.; Riviere, N. M.
1976
Absolute summability of Fourier transforms on $$R^n$$. Zbl 0327.42008
1976
Padé approximation of Stieltjes series. Zbl 0323.30044
Allen, G. D.; Chui, C. K.; Madych, W. R.; Narcowich, F. J.; Smith, P. W.
1975
On Littlewood-Paley functions. Zbl 0247.44005
1974
Padé approximation and orthogonal polynomials. Zbl 0279.41014
Allen, G. D.; Chui, C. K.; Madych, W. R.; Narcowich, F. J.; Smith, P. W.
1974
Allen, G. D.; Chui, C. K.; Madych, W. R.; Narcowich, F. J.; Smith, P. W.
1974
Iterated Littlewood-Paley functions and a multiplier theorem. Zbl 0292.42006
1974
all top 5

all top 5

### Cited in 188 Serials

 78 Engineering Analysis with Boundary Elements 46 Journal of Approximation Theory 40 Computers & Mathematics with Applications 36 Applied and Computational Harmonic Analysis 30 Applied Mathematics and Computation 23 Journal of Computational and Applied Mathematics 21 The Journal of Fourier Analysis and Applications 20 Advances in Computational Mathematics 16 Proceedings of the American Mathematical Society 15 Journal of Mathematical Analysis and Applications 14 International Journal for Numerical Methods in Engineering 14 International Journal of Wavelets, Multiresolution and Information Processing 13 Constructive Approximation 12 Mathematics of Computation 12 Applied Numerical Mathematics 11 Journal of Computational Physics 11 Applied Mathematical Modelling 10 Transactions of the American Mathematical Society 10 Numerical Algorithms 9 Numerische Mathematik 7 Computer Methods in Applied Mechanics and Engineering 7 The Journal of Geometric Analysis 6 Acta Applicandae Mathematicae 6 Mathematical and Computer Modelling 6 SIAM Journal on Mathematical Analysis 6 Computational and Applied Mathematics 6 Acta Mathematica Sinica. English Series 5 Mathematics and Computers in Simulation 4 Journal of Functional Analysis 4 Numerical Functional Analysis and Optimization 4 Acta Mathematicae Applicatae Sinica. English Series 4 Numerical Methods for Partial Differential Equations 4 Linear Algebra and its Applications 4 Fractals 4 Computational Methods for Differential Equations 3 Mathematical Notes 3 Advances in Mathematics 3 Archiv der Mathematik 3 Calcolo 3 Geometriae Dedicata 3 Mathematische Nachrichten 3 SIAM Journal on Numerical Analysis 3 Tôhoku Mathematical Journal. Second Series 3 Computational Mechanics 3 Journal of Scientific Computing 3 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 3 Analysis and Applications (Singapore) 3 Proceedings of the Steklov Institute of Mathematics 3 Science China. Mathematics 3 International Journal of Applied and Computational Mathematics 2 Analysis Mathematica 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 Mathematical Methods in the Applied Sciences 2 Arkiv för Matematik 2 Chaos, Solitons and Fractals 2 The Annals of Statistics 2 Journal of Multivariate Analysis 2 Mathematische Zeitschrift 2 Monatshefte für Mathematik 2 Results in Mathematics 2 Discrete & Computational Geometry 2 Applied Mathematics Letters 2 Science in China. Series A 2 Boletim da Sociedade Brasileira de Matemática. Nova Série 2 Applied Mathematics. Series B (English Edition) 2 Communications in Numerical Methods in Engineering 2 International Journal of Numerical Methods for Heat & Fluid Flow 2 Nonlinear Dynamics 2 Abstract and Applied Analysis 2 Communications in Nonlinear Science and Numerical Simulation 2 The ANZIAM Journal 2 Foundations of Computational Mathematics 2 Journal of Applied Mathematics 2 Sampling Theory in Signal and Image Processing 2 Analysis in Theory and Applications 2 Mediterranean Journal of Mathematics 2 SIAM Journal on Imaging Sciences 2 $$p$$-Adic Numbers, Ultrametric Analysis, and Applications 2 Analysis and Mathematical Physics 2 Journal of the Korean Society for Industrial and Applied Mathematics 2 Axioms 1 Applicable Analysis 1 Bulletin of the Australian Mathematical Society 1 Computers and Fluids 1 Communications in Mathematical Physics 1 International Journal of General Systems 1 International Journal for Numerical Methods in Fluids 1 International Journal of Systems Science 1 Inverse Problems 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Nonlinearity 1 Rocky Mountain Journal of Mathematics 1 Ukrainian Mathematical Journal 1 Wave Motion 1 The Mathematical Intelligencer 1 Applied Mathematics and Optimization 1 Automatica 1 Canadian Journal of Mathematics 1 Canadian Mathematical Bulletin ...and 88 more Serials
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### Cited in 48 Fields

 345 Numerical analysis (65-XX) 203 Harmonic analysis on Euclidean spaces (42-XX) 201 Approximations and expansions (41-XX) 118 Partial differential equations (35-XX) 52 Fluid mechanics (76-XX) 42 Functional analysis (46-XX) 42 Information and communication theory, circuits (94-XX) 31 Measure and integration (28-XX) 28 Integral transforms, operational calculus (44-XX) 28 Mechanics of deformable solids (74-XX) 22 Convex and discrete geometry (52-XX) 21 Integral equations (45-XX) 20 Operator theory (47-XX) 14 Real functions (26-XX) 14 Abstract harmonic analysis (43-XX) 14 Probability theory and stochastic processes (60-XX) 14 Statistics (62-XX) 14 Biology and other natural sciences (92-XX) 12 Number theory (11-XX) 12 Classical thermodynamics, heat transfer (80-XX) 11 Functions of a complex variable (30-XX) 11 Computer science (68-XX) 10 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Combinatorics (05-XX) 9 Ordinary differential equations (34-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Geophysics (86-XX) 8 Potential theory (31-XX) 8 Difference and functional equations (39-XX) 7 Operations research, mathematical programming (90-XX) 6 Topological groups, Lie groups (22-XX) 6 Sequences, series, summability (40-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 5 Group theory and generalizations (20-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 3 Manifolds and cell complexes (57-XX) 3 Systems theory; control (93-XX) 2 General topology (54-XX) 2 Quantum theory (81-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Differential geometry (53-XX) 1 Algebraic topology (55-XX) 1 Optics, electromagnetic theory (78-XX) 1 Mathematics education (97-XX)