## Schaback, Robert

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 Author ID: schaback.robert Published as: Schaback, Robert; Schaback, R.; Schaback, Robert A. more...less Homepage: https://num.math.uni-goettingen.de/schaback/ External Links: MGP · Wikidata · Google Scholar · dblp · GND · IdRef
 Documents Indexed: 129 Publications since 1970, including 7 Books 2 Contributions as Editor Co-Authors: 46 Co-Authors with 67 Joint Publications 1,034 Co-Co-Authors
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### Co-Authors

 63 single-authored 7 Wendland, Holger 6 Bozzini, Mira 6 Hon, Yiu-Chung 5 Lenarduzzi, Licia 5 Ling, Leevan 4 Rossini, Milvia 4 Wu, Zongmin 3 Davydov, Oleg V. 3 Mirzaei, Davoud 3 Mohammadi, Maryam Beyg 3 Werner, Helmut 2 Böhmer, Klaus 2 Braess, Dietrich 2 De Marchi, Stefano 2 Franke, Carsten 2 Narcowich, Francis J. 2 Pazouki, Maryam 2 Qi, Dongxu 2 Ward, Joseph Dinneen 2 Zwicknagl, Barbara Maria 1 Buhmann, Martin Dietrich 1 Bürger, Heiko 1 Chen, Ching-Shyang 1 Cheung, Ka Chun 1 Dehghan Takht Fooladi, Mehdi 1 Dereli, Yılmaz 1 Diener, Immo 1 Ebert, Jürgen 1 Golberg, Michael A. 1 Haußmann, Werner 1 Jetter, Kurt 1 Lee, Cheng-Feng 1 Mokhtari, Reza 1 Mouattamid, Mohammed 1 Müller, Stefan 1 Opfer, Roland 1 Rieger, Christian 1 Robitzsch, H. 1 Saberi Zafarghandi, Fahimeh 1 Santin, Gabriele 1 Scherer, Karl 1 Scheuerer, Michael 1 Schlather, Martin 1 Stöckler, Joachim 1 Volontè, Elena 1 Zhong, Min 1 Zhou, Xu
all top 5

### Serials

 15 Advances in Computational Mathematics 9 Journal of Approximation Theory 7 Journal of Computational and Applied Mathematics 7 Numerische Mathematik 6 Numerical Algorithms 5 Applied Mathematics and Computation 4 IMA Journal of Numerical Analysis 4 SIAM Journal on Numerical Analysis 4 Constructive Approximation 3 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 3 Computer Aided Geometric Design 2 Computers & Mathematics with Applications 2 Mathematics of Computation 2 Computing 2 Mathematische Zeitschrift 2 Applied Numerical Mathematics 1 Mathematical Methods in the Applied Sciences 1 Calcolo 1 Mitteilungen - Gauß-Gesellschaft Göttingen 1 International Journal for Numerical Methods in Engineering 1 Journal of Optimization Theory and Applications 1 SIAM Journal on Computing 1 Advances in Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Approximation Theory and its Applications 1 European Journal of Applied Mathematics 1 Applied and Computational Harmonic Analysis 1 Annals of Numerical Mathematics 1 Engineering Analysis with Boundary Elements 1 CMES. Computer Modeling in Engineering & Sciences 1 Analysis in Theory and Applications 1 Acta Numerica 1 Lecture Notes in Mathematics 1 Studies in Computational Mathematics 1 Springer-Lehrbuch
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### Fields

 100 Numerical analysis (65-XX) 68 Approximations and expansions (41-XX) 20 Partial differential equations (35-XX) 7 Computer science (68-XX) 6 Functional analysis (46-XX) 6 Operations research, mathematical programming (90-XX) 3 History and biography (01-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Integral equations (45-XX) 2 General and overarching topics; collections (00-XX) 2 Operator theory (47-XX) 2 Statistics (62-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Real functions (26-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Geometry (51-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Biology and other natural sciences (92-XX)

### Citations contained in zbMATH Open

110 Publications have been cited 2,675 times in 1,461 Documents Cited by Year
Error estimates and condition numbers for radial basis function interpolation. Zbl 0861.65007
Schaback, Robert
1995
Local error estimates for radial basis function interpolation of scattered data. Zbl 0762.41006
Wu, Zong-Min; Schaback, Robert
1993
Solving partial differential equations by collocation using radial basis functions. Zbl 0943.65133
Franke, C.; Schaback, R.
1998
Convergence order estimates of meshless collocation methods using radial basis functions. Zbl 0909.65088
Franke, Carsten; Schaback, Robert
1998
On unsymmetric collocation by radial basis functions. Zbl 1026.65107
Hon, Y. C.; Schaback, R.
2001
On generalized moving least squares and diffuse derivatives. Zbl 1252.65037
Mirzaei, Davoud; Schaback, Robert; Dehghan, Mehdi
2012
Kernel techniques: from machine learning to meshless methods. Zbl 1111.65108
Schaback, Robert; Wendland, Holger
2006
Shape preserving properties and convergence of univariate multiquadric quasi-interpolation. Zbl 0822.41025
Wu, Zongmin; Schaback, Robert
1994
Results on meshless collocation techniques. Zbl 1195.65177
Ling, Leevan; Opfer, Roland; Schaback, Robert
2006
Multivariate interpolation by polynomials and radial basis functions. Zbl 1076.41003
Schaback, Robert
2005
Convergence of unsymmetric kernel-based meshless collocation methods. Zbl 1165.65066
Schaback, Robert
2007
Multivariate interpolation and approximation by translates of a basis function. Zbl 1139.41301
Schaback, Robert
1995
Adaptive greedy techniques for approximate solution of large RBF systems. Zbl 0957.65021
Schaback, Robert; Wendland, Holger
2000
Improved error bounds for scattered data interpolation by radial basis functions. Zbl 0917.41011
Schaback, R.
1999
Creating surfaces from scattered data using radial basis functions. Zbl 0835.65036
Schaback, R.
1995
Direct meshless local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation. Zbl 1263.65118
Mirzaei, Davoud; Schaback, Robert
2013
Stable and convergent unsymmetric meshless collocation methods. Zbl 1167.65059
Ling, Leevan; Schaback, Robert
2008
Native Hilbert spaces for radial basis functions. I. Zbl 0944.46017
Schaback, Robert
1999
Bases for kernel-based spaces. Zbl 1234.41003
Pazouki, Maryam; Schaback, Robert
2011
Near-optimal data-independent point locations for radial basis function interpolation. Zbl 1070.65008
Marchi, Stefano; Schaback, Robert; Wendland, Holger
2005
An adaptive greedy algorithm for solving large RBF collocation problems. Zbl 1019.65093
Hon, Y. C.; Schaback, R.; Zhou, X.
2003
Characterization and construction of radial basis functions. Zbl 1035.41013
Schaback, Robert; Wendland, Holger
2001
Approximation by radial basis functions with finitely many centers. Zbl 0855.41011
Schaback, R.
1996
Operators on radial functions. Zbl 0857.42004
Schaback, Robert; Wu, Z.
1996
An improved subspace selection algorithm for meshless collocation methods. Zbl 1183.65153
Ling, Leevan; Schaback, Robert
2009
Interpolation of spatial data – a stochastic or a deterministic problem? Zbl 1426.62284
Scheuerer, M.; Schaback, R.; Schlather, M.
2013
Solving heat conduction problems by the direct meshless local Petrov-Galerkin (DMLPG) method. Zbl 1292.65107
Mirzaei, Davoud; Schaback, Robert
2014
A unified theory of radial basis functions. Native Hilbert spaces for radial basis functions. II. Zbl 0984.46014
Schaback, Robert
2000
Stability of kernel-based interpolation. Zbl 1188.41001
De Marchi, Stefano; Schaback, Robert
2010
Interpolation with variably scaled kernels. Zbl 1309.65015
Bozzini, Mira; Lenarduzzi, Licia; Rossini, Milvia; Schaback, Robert
2015
On convergent numerical algorithms for unsymmetric collocation. Zbl 1168.65419
Lee, Cheng-Feng; Ling, Leevan; Schaback, Robert
2009
A Newton basis for kernel spaces. Zbl 1185.41004
Müller, Stefan; Schaback, Robert
2009
Unsymmetric meshless methods for operator equations. Zbl 1187.65056
Schaback, Robert
2010
Error bounds for kernel-based numerical differentiation. Zbl 1335.65038
Davydov, Oleg; Schaback, Robert
2016
Lower bounds for norms of inverses of interpolation matrices for radial basis functions. Zbl 0829.41020
Schaback, Robert
1994
Bozzini, Mira; Lenarduzzi, Licia; Schaback, Robert
2002
The missing Wendland functions. Zbl 1229.41020
Schaback, Robert
2011
Interpolation with piecewise quadratic visually $$C^ 2$$ Bézier polynomials. Zbl 0675.41006
Schaback, Robert
1989
Spezielle rationale Splinefunktionen. Zbl 0252.41009
Schaback, Robert
1973
Inverse and saturation theorems for radial basis function interpolation. Zbl 0989.41002
Schaback, Robert; Wendland, Holger
2002
Limit problems for interpolation by analytic radial basis functions. Zbl 1129.41002
Schaback, Robert
2008
Approximation in Sobolev spaces by kernel expansions. Zbl 1022.46023
Narcowich, F. J.; Schaback, R.; Ward, J. D.
2002
On the efficiency of interpolation by radial basis functions. Zbl 0937.65013
Schaback, Robert
1997
All well-posed problems have uniformly stable and convergent discretizations. Zbl 1338.65138
Schaback, Robert
2016
Interpolation by basis functions of different scales and shapes. Zbl 1168.65315
Bozzini, M.; Lenarduzzi, L.; Rossini, M.; Schaback, R.
2004
Construction techniques for highly accurate quasi-interpolation operators. Zbl 0904.41012
Schaback, Robert; Wu, Zongmin
1997
A computational tool for comparing all linear PDE solvers. Zbl 1317.65228
Schaback, Robert
2015
A meshless method for solving the 2D Brusselator reaction-diffusion system. Zbl 1357.65152
Mohammadi, M.; Mokhtari, R.; Schaback, R.
2014
$$H^2$$-convergence of least-squares kernel collocation methods. Zbl 1436.65020
Cheung, Ka Chun; Ling, Leevan; Schaback, Robert
2018
Sampling and stability. Zbl 1274.65022
Rieger, Christian; Schaback, Robert; Zwicknagl, Barbara
2010
Recent developments in the dual reciprocity method using compactly supported radial basis functions. Zbl 1043.65133
Chen, C. S.; Golberg, M. A.; Schaback, Robert A.
2003
Solvability of partial differential equations by meshless kernel methods. Zbl 1136.65111
Hon, Y. C.; Schaback, Robert
2008
On alternation numbers in nonlinear Chebyshev approximation. Zbl 0395.41013
Schaback, Robert
1978
Solving the Laplace equation by meshless collocation using harmonic kernels. Zbl 1180.65161
Schaback, Robert
2009
Generalized Whittle-Matérn and polyharmonic kernels. Zbl 1272.41001
Bozzini, Mira; Rossini, Milvia; Schaback, Robert
2013
Multilevel interpolation and approximation. Zbl 0936.41002
Narcowich, F. J.; Schaback, R.; Ward, J. D.
1999
Stability of radial basis function interpolants. Zbl 1031.41003
Schaback, Robert
2002
The meshless kernel-based method of lines for solving the equal width equation. Zbl 1282.76086
Dereli, Yılmaz; Schaback, Robert
2013
Approximation by positive definite kernels. Zbl 1046.41011
Schaback, Robert; Wendland, Holger
2003
Minimal numerical differentiation formulas. Zbl 1478.65012
Davydov, Oleg; Schaback, Robert
2018
Optimal stencils in Sobolev spaces. Zbl 1483.65170
Davydov, Oleg; Schaback, Robert
2019
Solving the 3D Laplace equation by meshless collocation via harmonic kernels. Zbl 1272.65096
Hon, Y. C.; Schaback, R.
2013
Schaback, Robert
1990
Planar curve interpolation by piecewise conics of arbitrary type. Zbl 0782.41007
Schaback, Robert
1993
Error analysis of nodal meshless methods. Zbl 1406.65131
Schaback, Robert
2017
Greedy sparse linear approximations of functionals from nodal data. Zbl 1305.65102
Schaback, Robert
2014
Interpolation mit nichtlinearen Klassen von Spline-Funktionen. Zbl 0259.41002
Schaback, Robert
1973
Superconvergence of kernel-based interpolation. Zbl 1400.41003
Schaback, Robert
2018
Recursive kernels. Zbl 1212.46053
Mouattamid, Mohammed; Schaback, Robert
2009
Linearly constrained reconstruction of functions by kernels with applications to machine learning. Zbl 1106.65008
Schaback, R.; Werner, J.
2006
The meshless kernel-based method of lines for parabolic equations. Zbl 1369.65109
Hon, Y. C.; Schaback, R.; Zhong, M.
2014
Radial basis functions viewed from cubic splines. Zbl 0889.41006
Schaback, Robert
1997
Remarks on meshless local construction of surfaces. Zbl 0967.65016
Schaback, Robert
2000
Approximation of eigenfunctions in kernel-based spaces. Zbl 1353.65139
Santin, G.; Schaback, R.
2016
Interpolation and approximation in Taylor spaces. Zbl 1290.41014
Zwicknagl, Barbara; Schaback, Robert
2013
Recovery of functions from weak data using unsymmetric meshless kernel-based methods. Zbl 1141.65010
Schaback, Robert
2008
Praktische Mathematik. II: Methoden der Analysis. Nach Vorlesungen an der Universität Münster, herausgegeben mit Unterstützung von R. Runge und H. Arnst. Zbl 0259.65001
Werner, Helmut; Schaback, Robert
1972
Konstruktion und algebraische Eigenschaften von M-Spline- Interpolierenden. Zbl 0267.65007
Schaback, Robert
1973
A nonlinear discretization theory. Zbl 1290.65107
Böhmer, Klaus; Schaback, Robert
2013
A meshfree method for solving the Monge-Ampère equation. Zbl 1425.35069
Böhmer, Klaus; Schaback, Robert
2019
Convergence analysis of general spectral methods. Zbl 1353.65095
2017
Numerical mathematics. 4., vollst. überarb. Aufl. (Numerische Mathematik.) Zbl 0746.65003
Schaback, Robert; Werner, Helmut
1992
Geometrical differentiation and high-accuracy curve interpolation. Zbl 0747.41003
Schaback, Robert
1992
Error estimates for approximations from control nets. Zbl 0765.65015
Schaback, Robert
1993
On the expected sublinearity of the Boyer-Moore algorithm. Zbl 0651.68072
Schaback, R.
1988
Convergence analysis of the general Gauss-Newton algorithm. Zbl 0543.65029
Schaback, Robert
1985
Approximation of polynomials by radial basis functions. Zbl 0826.41022
Schaback, Robert
1994
Optimal nodes for interpolation in Hardy spaces. Zbl 0458.41002
Schaback, Robert
1982
Praktische Mathematik II. Methoden der Analysis. Nach Vorlesungen an den Universitäten Münster und Göttingen hrsg. mit Unterstützung von J. Ebert. 2., neubearb. u. erw. Aufl. Zbl 0383.65001
Werner, Helmut; Schaback, Robert
1979
On global $$GC^ 2$$ convexity preserving interpolation of planar curves by piecewise Bézier polynomials. Zbl 0675.41007
Schaback, R.
1989
An extended continuous Newton method. Zbl 0688.90048
Diener, I.; Schaback, R.
1990
Optimal geometric Hermite interpolation of curves. Zbl 0905.65009
Schaback, Robert
1998
Radial kernels via scale derivatives. Zbl 1317.65262
Bozzini, Mira; Rossini, Milvia; Schaback, Robert; Volontè, Elena
2015
Calculation of best approximations by rational splines. Zbl 0354.41013
Schaback, R.
1976
Globale Konvergenz von Verfahren zur nichtlinearen Approximation. Zbl 0357.65010
Schaback, R.
1976
Suboptimal exponential approximations. Zbl 0428.65004
Schaback, Robert
1979
Bases for conditionally positive definite kernels. Zbl 1259.41008
Pazouki, Maryam; Schaback, Robert
2013
Kernel $$B$$-splines and interpolation. Zbl 1090.65014
Bozzini, M.; Lenarduzzi, L.; Schaback, R.
2006
Optimale Interpolations- und Approximationssysteme. Zbl 0248.65037
Schaback, Robert
1973
Eine rundungsgenaue Formel zur maschinellen Berechnung der Prager-Oettli- Schranke. Zbl 0383.65023
Schaback, R.
1978
Optimal stencils in Sobolev spaces. Zbl 1483.65170
Davydov, Oleg; Schaback, Robert
2019
A meshfree method for solving the Monge-Ampère equation. Zbl 1425.35069
Böhmer, Klaus; Schaback, Robert
2019
On the fractional derivatives of radial basis functions: theories and applications. Zbl 1423.35423
Zafarghandi, Fahimeh Saberi; Mohammadi, Maryam; Schaback, Robert
2019
$$H^2$$-convergence of least-squares kernel collocation methods. Zbl 1436.65020
Cheung, Ka Chun; Ling, Leevan; Schaback, Robert
2018
Minimal numerical differentiation formulas. Zbl 1478.65012
Davydov, Oleg; Schaback, Robert
2018
Superconvergence of kernel-based interpolation. Zbl 1400.41003
Schaback, Robert
2018
Error analysis of nodal meshless methods. Zbl 1406.65131
Schaback, Robert
2017
Convergence analysis of general spectral methods. Zbl 1353.65095
2017
Kernel-based adaptive approximation of functions with discontinuities. Zbl 1411.65024
Lenarduzzi, Licia; Schaback, Robert
2017
Error bounds for kernel-based numerical differentiation. Zbl 1335.65038
Davydov, Oleg; Schaback, Robert
2016
All well-posed problems have uniformly stable and convergent discretizations. Zbl 1338.65138
Schaback, Robert
2016
Approximation of eigenfunctions in kernel-based spaces. Zbl 1353.65139
Santin, G.; Schaback, R.
2016
Interpolation with variably scaled kernels. Zbl 1309.65015
Bozzini, Mira; Lenarduzzi, Licia; Rossini, Milvia; Schaback, Robert
2015
A computational tool for comparing all linear PDE solvers. Zbl 1317.65228
Schaback, Robert
2015
Radial kernels via scale derivatives. Zbl 1317.65262
Bozzini, Mira; Rossini, Milvia; Schaback, Robert; Volontè, Elena
2015
Direct meshless kernel techniques for time-dependent equations. Zbl 1339.65190
Hon, Y. C.; Schaback, R.
2015
Solving heat conduction problems by the direct meshless local Petrov-Galerkin (DMLPG) method. Zbl 1292.65107
Mirzaei, Davoud; Schaback, Robert
2014
A meshless method for solving the 2D Brusselator reaction-diffusion system. Zbl 1357.65152
Mohammadi, M.; Mokhtari, R.; Schaback, R.
2014
Greedy sparse linear approximations of functionals from nodal data. Zbl 1305.65102
Schaback, Robert
2014
The meshless kernel-based method of lines for parabolic equations. Zbl 1369.65109
Hon, Y. C.; Schaback, R.; Zhong, M.
2014
Carl Friedrich Gauß’s contributions to numerical mathematics. (Die Beiträge von Carl Friedrich Gauß zur numerischen Mathematik.) Zbl 1304.01028
Schaback, Robert
2014
Direct meshless local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation. Zbl 1263.65118
Mirzaei, Davoud; Schaback, Robert
2013
Interpolation of spatial data – a stochastic or a deterministic problem? Zbl 1426.62284
Scheuerer, M.; Schaback, R.; Schlather, M.
2013
Generalized Whittle-Matérn and polyharmonic kernels. Zbl 1272.41001
Bozzini, Mira; Rossini, Milvia; Schaback, Robert
2013
The meshless kernel-based method of lines for solving the equal width equation. Zbl 1282.76086
Dereli, Yılmaz; Schaback, Robert
2013
Solving the 3D Laplace equation by meshless collocation via harmonic kernels. Zbl 1272.65096
Hon, Y. C.; Schaback, R.
2013
Interpolation and approximation in Taylor spaces. Zbl 1290.41014
Zwicknagl, Barbara; Schaback, Robert
2013
A nonlinear discretization theory. Zbl 1290.65107
Böhmer, Klaus; Schaback, Robert
2013
Bases for conditionally positive definite kernels. Zbl 1259.41008
Pazouki, Maryam; Schaback, Robert
2013
On generalized moving least squares and diffuse derivatives. Zbl 1252.65037
Mirzaei, Davoud; Schaback, Robert; Dehghan, Mehdi
2012
Bases for kernel-based spaces. Zbl 1234.41003
Pazouki, Maryam; Schaback, Robert
2011
The missing Wendland functions. Zbl 1229.41020
Schaback, Robert
2011
Stability of kernel-based interpolation. Zbl 1188.41001
De Marchi, Stefano; Schaback, Robert
2010
Unsymmetric meshless methods for operator equations. Zbl 1187.65056
Schaback, Robert
2010
Sampling and stability. Zbl 1274.65022
Rieger, Christian; Schaback, Robert; Zwicknagl, Barbara
2010
An improved subspace selection algorithm for meshless collocation methods. Zbl 1183.65153
Ling, Leevan; Schaback, Robert
2009
On convergent numerical algorithms for unsymmetric collocation. Zbl 1168.65419
Lee, Cheng-Feng; Ling, Leevan; Schaback, Robert
2009
A Newton basis for kernel spaces. Zbl 1185.41004
Müller, Stefan; Schaback, Robert
2009
Solving the Laplace equation by meshless collocation using harmonic kernels. Zbl 1180.65161
Schaback, Robert
2009
Recursive kernels. Zbl 1212.46053
Mouattamid, Mohammed; Schaback, Robert
2009
Stable and convergent unsymmetric meshless collocation methods. Zbl 1167.65059
Ling, Leevan; Schaback, Robert
2008
Limit problems for interpolation by analytic radial basis functions. Zbl 1129.41002
Schaback, Robert
2008
Solvability of partial differential equations by meshless kernel methods. Zbl 1136.65111
Hon, Y. C.; Schaback, Robert
2008
Recovery of functions from weak data using unsymmetric meshless kernel-based methods. Zbl 1141.65010
Schaback, Robert
2008
Convergence of unsymmetric kernel-based meshless collocation methods. Zbl 1165.65066
Schaback, Robert
2007
Kernel techniques: from machine learning to meshless methods. Zbl 1111.65108
Schaback, Robert; Wendland, Holger
2006
Results on meshless collocation techniques. Zbl 1195.65177
Ling, Leevan; Opfer, Roland; Schaback, Robert
2006
Linearly constrained reconstruction of functions by kernels with applications to machine learning. Zbl 1106.65008
Schaback, R.; Werner, J.
2006
Kernel $$B$$-splines and interpolation. Zbl 1090.65014
Bozzini, M.; Lenarduzzi, L.; Schaback, R.
2006
Topics in multivariate approximation and interpolation. Zbl 1205.41002
2006
Multivariate interpolation by polynomials and radial basis functions. Zbl 1076.41003
Schaback, Robert
2005
Near-optimal data-independent point locations for radial basis function interpolation. Zbl 1070.65008
Marchi, Stefano; Schaback, Robert; Wendland, Holger
2005
Numerical mathematics. 5th completely new revised ed. (Numerische Mathematik.) Zbl 1060.65003
Schaback, Robert; Wendland, Holger
2005
Interpolation by basis functions of different scales and shapes. Zbl 1168.65315
Bozzini, M.; Lenarduzzi, L.; Rossini, M.; Schaback, R.
2004
An adaptive greedy algorithm for solving large RBF collocation problems. Zbl 1019.65093
Hon, Y. C.; Schaback, R.; Zhou, X.
2003
Recent developments in the dual reciprocity method using compactly supported radial basis functions. Zbl 1043.65133
Chen, C. S.; Golberg, M. A.; Schaback, Robert A.
2003
Approximation by positive definite kernels. Zbl 1046.41011
Schaback, Robert; Wendland, Holger
2003
Bozzini, Mira; Lenarduzzi, Licia; Schaback, Robert
2002
Inverse and saturation theorems for radial basis function interpolation. Zbl 0989.41002
Schaback, Robert; Wendland, Holger
2002
Approximation in Sobolev spaces by kernel expansions. Zbl 1022.46023
Narcowich, F. J.; Schaback, R.; Ward, J. D.
2002
Stability of radial basis function interpolants. Zbl 1031.41003
Schaback, Robert
2002
On unsymmetric collocation by radial basis functions. Zbl 1026.65107
Hon, Y. C.; Schaback, R.
2001
Characterization and construction of radial basis functions. Zbl 1035.41013
Schaback, Robert; Wendland, Holger
2001
Adaptive greedy techniques for approximate solution of large RBF systems. Zbl 0957.65021
Schaback, Robert; Wendland, Holger
2000
A unified theory of radial basis functions. Native Hilbert spaces for radial basis functions. II. Zbl 0984.46014
Schaback, Robert
2000
Remarks on meshless local construction of surfaces. Zbl 0967.65016
Schaback, Robert
2000
Improved error bounds for scattered data interpolation by radial basis functions. Zbl 0917.41011
Schaback, R.
1999
Native Hilbert spaces for radial basis functions. I. Zbl 0944.46017
Schaback, Robert
1999
Multilevel interpolation and approximation. Zbl 0936.41002
Narcowich, F. J.; Schaback, R.; Ward, J. D.
1999
Solving partial differential equations by collocation using radial basis functions. Zbl 0943.65133
Franke, C.; Schaback, R.
1998
Convergence order estimates of meshless collocation methods using radial basis functions. Zbl 0909.65088
Franke, Carsten; Schaback, Robert
1998
Optimal geometric Hermite interpolation of curves. Zbl 0905.65009
Schaback, Robert
1998
On the efficiency of interpolation by radial basis functions. Zbl 0937.65013
Schaback, Robert
1997
Construction techniques for highly accurate quasi-interpolation operators. Zbl 0904.41012
Schaback, Robert; Wu, Zongmin
1997
Radial basis functions viewed from cubic splines. Zbl 0889.41006
Schaback, Robert
1997
Optimal recovery in translation-invariant spaces of functions. Zbl 0889.41002
Schaback, R.
1997
Approximation by radial basis functions with finitely many centers. Zbl 0855.41011
Schaback, R.
1996
Operators on radial functions. Zbl 0857.42004
Schaback, Robert; Wu, Z.
1996
Error estimates and condition numbers for radial basis function interpolation. Zbl 0861.65007
Schaback, Robert
1995
Multivariate interpolation and approximation by translates of a basis function. Zbl 1139.41301
Schaback, Robert
1995
Creating surfaces from scattered data using radial basis functions. Zbl 0835.65036
Schaback, R.
1995
Shape preserving properties and convergence of univariate multiquadric quasi-interpolation. Zbl 0822.41025
Wu, Zongmin; Schaback, Robert
1994
Lower bounds for norms of inverses of interpolation matrices for radial basis functions. Zbl 0829.41020
Schaback, Robert
1994
Approximation of polynomials by radial basis functions. Zbl 0826.41022
Schaback, Robert
1994
Local error estimates for radial basis function interpolation of scattered data. Zbl 0762.41006
Wu, Zong-Min; Schaback, Robert
1993
Planar curve interpolation by piecewise conics of arbitrary type. Zbl 0782.41007
Schaback, Robert
1993
Error estimates for approximations from control nets. Zbl 0765.65015
Schaback, Robert
1993
A parallel multistage method for surface/surface intersection. Zbl 0779.65095
Bürger, Heiko; Schaback, Robert
1993
Numerical mathematics. 4., vollst. überarb. Aufl. (Numerische Mathematik.) Zbl 0746.65003
Schaback, Robert; Werner, Helmut
1992
Geometrical differentiation and high-accuracy curve interpolation. Zbl 0747.41003
Schaback, Robert
1992
Schaback, Robert
1990
An extended continuous Newton method. Zbl 0688.90048
Diener, I.; Schaback, R.
1990
Interpolation with piecewise quadratic visually $$C^ 2$$ Bézier polynomials. Zbl 0675.41006
Schaback, Robert
1989
On global $$GC^ 2$$ convexity preserving interpolation of planar curves by piecewise Bézier polynomials. Zbl 0675.41007
Schaback, R.
1989
Convergence of planar curve interpolation schemes. Zbl 0726.41004
Schaback, Robert
1989
On the expected sublinearity of the Boyer-Moore algorithm. Zbl 0651.68072
Schaback, R.
1988
Convergence analysis of the general Gauss-Newton algorithm. Zbl 0543.65029
Schaback, Robert
1985
Optimal nodes for interpolation in Hardy spaces. Zbl 0458.41002
Schaback, Robert
1982
Praktische Mathematik II. Methoden der Analysis. Nach Vorlesungen an den Universitäten Münster und Göttingen hrsg. mit Unterstützung von J. Ebert. 2., neubearb. u. erw. Aufl. Zbl 0383.65001
Werner, Helmut; Schaback, Robert
1979
Suboptimal exponential approximations. Zbl 0428.65004
Schaback, Robert
1979
...and 10 more Documents
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### Cited by 1,695 Authors

 61 Schaback, Robert 54 Dehghan Takht Fooladi, Mehdi 38 Ling, Leevan 34 Wu, Zongmin 27 Hon, Yiu-Chung 22 Chen, Ching-Shyang 21 Power, Henry 20 Cavoretto, Roberto 19 Wendland, Holger 18 Fasshauer, Gregory E. 17 De Marchi, Stefano 17 De Rossi, Alessandra 17 Siraj-ul-Islam 16 Abbaszadeh, Mostafa 16 Levesley, Jeremy 16 Mirzaei, Davoud 15 Fornberg, Bengt 15 Perracchione, Emma 14 Esmaeilbeigi, Mohsen 14 Kansa, Edward J. 13 Gao, Wenwu 13 Haq, Sirajul 13 Shivanian, Elyas 13 Uddin, Marjan 13 Ye, Qi 12 Abbasbandy, Saeid 12 Boyd, John Philip 12 Duan, Yong 12 Santin, Gabriele 12 Zhang, Shengliang 11 Chen, Wen 11 Larsson, Elisabeth 11 Li, Xiaolin 11 Narcowich, Francis J. 11 Nikan, Omid 11 Yoon, Jungho 10 Avazzadeh, Zakieh 10 Chen, Jiun-Shyan 10 Davydov, Oleg V. 10 Golbabai, Ahmad 10 Kindelan, Manuel Segura 10 Mohammadi, Vahid 10 Rieger, Christian 10 Ward, Joseph Dinneen 10 Wright, Grady B. 9 Ferreira, António Joaquim Mendes 9 Hu, Hsin-Yun 9 Porcu, Emilio 9 Rossini, Milvia 9 Wang, Lihua 8 Bozzini, Mira 8 Haasdonk, Bernard 8 Karvonen, Toni 8 Li, Jichun 8 Menegatto, Valdir Antonio 8 Sarra, Scott A. 8 Sun, Zhengjie 8 Tan, Yongji 8 Zhang, Yunxin 7 Bayona, Victor 7 Cao, Feilong 7 Flyer, Natasha 7 Heryudono, Alfa R. H. 7 Iske, Armin 7 Karageorghis, Andreas 7 Kazem, Saeed 7 Liu, Gui-Rong 7 Mohammadi, Maryam Beyg 7 Peron, Ana Paula 7 Rad, Jamal Amani 7 Šarler, Božidar 7 Trask, Nathaniel A. 7 Vianello, Marco 7 Zwicknagl, Barbara Maria 6 Beatson, Rick K. 6 Cheng, Alexander H.-D. 6 Chi, Sheng-Wei 6 Floater, Michael S. 6 Griebel, Michael 6 Le Gia, Quoc Thong 6 Liew, Kim Meow 6 Marchetti, Francesco 6 Moscoso, Miguel 6 Nürnberger, Günther 6 Särkkä, Simo 6 Shankar, Varun 6 Sloan, Ian Hugh 6 Sun, Xingping 6 Wang, Renhong 5 Ballestra, Luca Vincenzo 5 Bernal, Francisco 5 Buhmann, Martin Dietrich 5 Chang, Xiaolin 5 Chatrabgoun, Omid 5 Dereli, Yılmaz 5 Ghehsareh, Hadi Roohani 5 Golberg, Michael A. 5 González-Rodríguez, Pedro 5 He, Rui 5 Hubbert, Simon ...and 1,595 more Authors
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### Cited in 206 Serials

 214 Engineering Analysis with Boundary Elements 90 Applied Mathematics and Computation 88 Computers & Mathematics with Applications 75 Journal of Computational and Applied Mathematics 68 Journal of Computational Physics 56 Journal of Approximation Theory 50 Advances in Computational Mathematics 38 Applied Numerical Mathematics 33 Journal of Scientific Computing 31 Numerical Algorithms 28 Computer Methods in Applied Mechanics and Engineering 27 Numerische Mathematik 25 Applied Mathematical Modelling 23 International Journal for Numerical Methods in Engineering 22 Mathematics of Computation 21 Computational and Applied Mathematics 19 Computer Aided Geometric Design 15 Numerical Methods for Partial Differential Equations 15 International Journal of Computer Mathematics 15 SIAM Journal on Scientific Computing 14 BIT 14 Computational Mechanics 13 Constructive Approximation 13 International Journal of Computational Methods 12 SIAM/ASA Journal on Uncertainty Quantification 11 Computing 11 SIAM Journal on Numerical Analysis 11 Journal of Complexity 11 Applied Mathematics Letters 11 Applied and Computational Harmonic Analysis 10 Journal of Mathematical Analysis and Applications 9 Computational Methods for Differential Equations 8 Computers and Fluids 8 Communications in Nonlinear Science and Numerical Simulation 8 International Journal of Applied and Computational Mathematics 7 Analysis and Applications (Singapore) 6 Computer Physics Communications 6 Mathematics and Computers in Simulation 6 Numerical Functional Analysis and Optimization 6 Communications in Numerical Methods in Engineering 6 Mathematical Problems in Engineering 6 Journal of Mathematical Modeling 5 Mathematical Methods in the Applied Sciences 5 The Journal of Fourier Analysis and Applications 5 Science China. Mathematics 5 Statistics and Computing 4 Acta Mechanica 4 Applicable Analysis 4 Journal of Global Optimization 4 Electronic Journal of Statistics 4 International Journal for Computational Methods in Engineering Science and Mechanics 4 Advances in Applied Mathematics and Mechanics 3 International Journal for Numerical Methods in Fluids 3 Journal of Multivariate Analysis 3 Mathematische Zeitschrift 3 Acta Applicandae Mathematicae 3 SIAM Journal on Matrix Analysis and Applications 3 Linear Algebra and its Applications 3 SIAM Journal on Mathematical Analysis 3 Computational Statistics and Data Analysis 3 Applied Mathematics. Series B (English Edition) 3 International Journal of Numerical Methods for Heat & Fluid Flow 3 Nonlinear Dynamics 3 Abstract and Applied Analysis 3 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 3 Foundations of Computational Mathematics 3 Journal of Applied Mathematics 3 SIAM Journal on Applied Dynamical Systems 3 Analysis in Theory and Applications 3 Advances in Difference Equations 3 Inverse Problems in Science and Engineering 3 Communications in Computational Physics 3 Mathematics 3 AIMS Mathematics 2 Inverse Problems 2 Mathematical Notes 2 Chaos, Solitons and Fractals 2 The Annals of Statistics 2 Calcolo 2 Journal of Optimization Theory and Applications 2 Results in Mathematics 2 Acta Mathematica Hungarica 2 Physica D 2 Journal of Economic Dynamics & Control 2 Machine Learning 2 Japan Journal of Industrial and Applied Mathematics 2 Journal of Mathematical Imaging and Vision 2 Potential Analysis 2 Computational Optimization and Applications 2 Numerical Linear Algebra with Applications 2 Filomat 2 European Journal of Mechanics. A. Solids 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 The ANZIAM Journal 2 Mathematical Modelling and Analysis 2 Iranian Journal of Science and Technology. Transaction A: Science 2 Multiscale Modeling & Simulation 2 Structural and Multidisciplinary Optimization 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications ...and 106 more Serials
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### Cited in 48 Fields

 1,117 Numerical analysis (65-XX) 382 Approximations and expansions (41-XX) 345 Partial differential equations (35-XX) 134 Fluid mechanics (76-XX) 113 Mechanics of deformable solids (74-XX) 73 Statistics (62-XX) 63 Functional analysis (46-XX) 56 Computer science (68-XX) 45 Probability theory and stochastic processes (60-XX) 44 Integral equations (45-XX) 42 Harmonic analysis on Euclidean spaces (42-XX) 34 Ordinary differential equations (34-XX) 28 Operations research, mathematical programming (90-XX) 28 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 25 Geophysics (86-XX) 23 Classical thermodynamics, heat transfer (80-XX) 23 Biology and other natural sciences (92-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 20 Real functions (26-XX) 20 Operator theory (47-XX) 20 Statistical mechanics, structure of matter (82-XX) 19 Information and communication theory, circuits (94-XX) 17 Optics, electromagnetic theory (78-XX) 13 Systems theory; control (93-XX) 12 Functions of a complex variable (30-XX) 12 Special functions (33-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Dynamical systems and ergodic theory (37-XX) 9 Quantum theory (81-XX) 8 Potential theory (31-XX) 8 Abstract harmonic analysis (43-XX) 7 Integral transforms, operational calculus (44-XX) 7 Global analysis, analysis on manifolds (58-XX) 4 Convex and discrete geometry (52-XX) 3 Combinatorics (05-XX) 3 Number theory (11-XX) 3 Measure and integration (28-XX) 3 Differential geometry (53-XX) 2 Commutative algebra (13-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Mechanics of particles and systems (70-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Geometry (51-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Mathematics education (97-XX)

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