R. Schaback's research page


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Research-oriented texts for advanced students: try here


Current incomplete projects          (preliminary  manuscripts available on request)

MATLAB Programming for Kernel-Based Methods    pdf

Scaling Radial Basis Functions (with E. Larsson, Univ. Uppsala) 

Convergence Analysis of General Spectral Methods (with Maryam Mohammadi, Isfahan University of Technology) 

The Meshless Kernel-Based Method of Lines for Solving Nonlinear Evolution Equations

Geometry of Kernel--Based Spaces 

Towards Kernel--Based Meshless Methods for the Incompressible Navier--Stokes Equation

Wavelets generated by Kernels via Scale Derivatives, with Mira Bozzini, Milvia Rossini, and Elena Volonte


Available preprints, sorted backwards in time, with links to pdf files. These files are early preprints, not in the finally published form!


Submitted preprints, partly under revision:

All Well--Posed Problems have Uniformly Stable and Convergent Discretizations, submitted, arxiv version of 2014/03/14, possibly newer:  pdf

Error Bounds for Kernel-Based Numerical Differentiation, with Oleg Davydov, Univ. of Strathclyde, in revision   pdf

On the fractional derivatives of Radial Basis Functions  (with Maryam Mohammadi, Isfahan University of Technology), submitted   pdf

Kernels via Scale Derivatives (with M. Bozzini, M. Rossini and E. Volonte, Univ. Milano-Biccocca), in revision,   pdf

Direct Meshless Kernel Techniques for Time--Dependent Equations, with Y.C. Hon, HongKong City Univ., in minor revision,    pdf

Finally accepted preprints, but without DOI or volume/page information:

A meshless method for solving the 2D Brusselator reaction-diffusion system
(with M. Mohammadi und R. Mokhtari, Isfahan University of Technology), 
accepted for publication in Computer Modeling in Engineering & Sciences (CMES),  pdf

Multivariate Approximation, to appear in: Encyclopedia of Applied and Computational Mathematics, Springer-Verlag Berlin Heidelberg  pdf

Shift-Invariant Approximation, to appear in: Encyclopedia of Applied and Computational Mathematics, Springer-Verlag Berlin Heidelberg  pdf


Published papers and books
Notes:

The Meshless Kernel-Based Method of Lines for Parabolic Equations, with Y.C. Hon, HongKong City Univ. and Min Zhong, Fudan U. Shanghai,
Computers and Mathematics with Applications 68 (2014), pp. 2057-2067 DOI information: 10.1016/j.camwa.2014.09.015   pdf

Die Beiträge von Carl-Friedrich Gauß zur Numerischen Mathematik, Mitteilungen der Gauß-Gesellschaft, Band 51, Göttingen 2014, p. 63-86,  pdf

A computational tool for comparing all linear PDE solvers  ( -  Error-optimal methods are meshless - ),  accepted by ACOM, DOI 10.1007/s10444-014-9360-5, programs   pdf

Interpolation with variably scaled kernels (with M. Bozzini. L. Lenarduzzi. and M. Rossini, Univ. Milano-Biccocca),
IMA Journal of Numerical Analysis 2014; doi: 10.1093/imanum/drt071
http://imajna.oxfordjournals.org/cgi/reprint/drt071?ijkey=zorzYIBcOzjHogr&keytype=ref   old submitted   pdf

Greedy Sparse Linear Approximations of Functionals from Nodal Data, DOI: 10.1007/s11075-013-9806-8,
Numerical Algorithms: Volume 67, Issue 3 (2014), Page 531-547, (with examples not in the final version: pdf)

Solving Heat Conduction Problems by the  Direct Meshless Local Petrov-Galerkin (DMLPG) method (with D. Mirzaei, Univ. of  Isfahan),
Numerical Algorithms 65 no. 2, 275-291, 2014, http://dx.doi.org/10.1007/s11075-013-9711-1,
http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s11075-013-9711-1[1]   pdf

Interpolation of spatial data - a stochastic or a deterministic problem?, with Michael Scheuerer and Martin Schlather,
European Journal of Applied Mathematics 24 Nr. 4, 2013, pp. 601-629 pdf

Generalized Whittle--Matern and Polyharmonic  Kernels, with Mira Bozzini and Milvia Rossini,  Univ. Milano-Biccocca,
Advances in Computational Mathematics: Volume 39, Issue 1 (2013), Page 129-141, http://dx.doi.org/10.1007/s10444-012-9277-9       online version   old pdf

Direct Discretizations with Applications to Meshless Methods for PDEs, Dolomites Research Notes on Approximation,
Proceedings of DWCAA12, Volume 6, 2013, p. 37-51, open access pdf, local  pdf

A Nonlinear Discretization Theory (with Klaus Böhmer, Marburg),
http://authors.elsevier.com/sd/article/S0377042713001374
Journal of Computational and Applied Mathematics 254, 2013, 204–219 ,  pdf

Interpolation and Approximation in Taylor Spaces (with B. Zwicknagl, Bonn), http://dx.doi.org/10.1016/j.jat.2013.03.006, 
J. of Approx. Th,Volume 171, July 2013, Pages 65–83  pdf

Helmut Werner. A vita for the website "History of Approximation Theory".  pdf

Publications of Helmut Werner. A commented list, for the website "History of Approximation Theory".  pdf 

Solving the 3D Laplace Equation by Meshless Collocation via Harmonic Kernels (with Y.C. Hon, Hong Kong City University),
Advances in Computational Mathematics: Volume 38, Issue 1 (2013), Page 1-19,  pdf

Direct Meshless Local Petrov-Galerkin (DMLPG) Method: A Generalized MLS Approximation, 2011  (with Davoud Mirzaei, Univ. of  Isfahan),
http://dx.doi.org/10.1016/j.apnum.2013.01.002, Applied Numerical Mathematics, 68, June 2013, Pages 73–82  pdf

Bases for Conditionally Positive Definite Kernels, with M. Pazouki,
CAM,  Volume 243, 1 May 2013, Pages 152–163 ,   http://dx.doi.org/10.1016/j.cam.2012.10.023  pdf    MATLAB  programs

The Meshless Kernel-Based Method of Lines for Solving the Equal Width Equation (with Y. Dereli, Anadolu University Eskişehir/ Turkey), 2010,
Appl. Math. and Comp., Volume 219, Issue 10, 15 January 2013, Pages 5224–5232,  http://dx.doi.org/10.1016/j.amc.2012.10.086   pdf MATLAB  

On Generalized Moving Least Squares and Diffuse Derivatives  (with D. Mirzaei and M. Dehghan, Univ. of  Isfahan),
IMA J. Numer. Anal. 32, No. 3, 983-1000 (2012). doi: 10.1093/imanum/drr030  OUP abstract OUP pdf     pdf

Direct Error Bounds for Symmeytic RBF Collocation, proceedings of "Meshless Methods in Science and Engineering" Porto, 2012 pdf

Bases for Kernel-Bases Spaces, with Maryam Pazouki, 2011, Computational and Applied Mathematics  236 (2011), pp. 575-588
available online,  via DOI  10.1016/j.cam.2011.05.021   programs  pdf

The Missing Wendland Functions, Advances in Computational Mathematics, 43 (2010),  67-81, DOI: 10.1007/s10444-009-9142-7,  pdf  Maple

Unsymmetric Meshless Methods for Operator Equations,
Numerische Mathematik 114 (2010), 629-651 DOI : 10.1007/s00211-009-0265-z  Springer online   pdf

Sampling and Stability (with C. Rieger and B. Zwicknagl, Bonn),
survey, in M. Dæhlen et al. (Eds.): Mathematical Methods for Curves and Surfaces 2008, online version
Lecture Notes in Computer Science 5862, pp. 347–369, 2010   pdf

Stability of Kernel-Based Interpolation (with Stefano de Marchi, Univ. Padova),
Adv. in Comp. Math. 32 (2010)  155-161, DOI    10.1007/s10444-008-9093-4
online version, and older version as  pdf    MATLAB zipfile

Nonstandard Kernels and Their Applications (with St. De Marchi, Univ. Padova),
DRNA (Dolomites Research Notes on Approximations) Vol. 2, 2009, pp. 16-43.,  pdf programs

An improved subspace selection algorithm for meshless collocation methods (with Leevan Ling, HongKong Baptist Univ.),
International Journal for Numerical Methods in Engineering 80 (2009) 1623 - 1639  DOI 10.1002/nme.2674   pdf

Recursive Kernels (with Mohammed Mouattamid),
Analysis in Theory and Applications 25, 2009, 301-316,  pdf

A Newton Basis for Kernel Spaces (with Stefan Müller),
J. Approx. Th. 161, 2009,  645-655,    pdf   MATLAB    Online version

Solving the Laplace Equation by Meshless Collocation Using Harmonic Kernels, 
Adv. in Comp. Math. 31, 2009, 457 - 470, DOI 10.1007/s10444-008-9078-3,  online via Springerlink, old version:   pdf    MATLAB

On Convergent Numerical Algorithms for Unsymmetric Collocation (with Cheng-Feng Lee and Leevan Ling), 
Adv. in Comp. Math. 30, 2009, 339-354, pdf

Stable and Convergent Unsymmetric Meshless Collocation Methods (with Leevan Ling),
SIAM J. Numer. Anal., Vol. 46, No. 3, 1097-1115, 2008  pdf

An adaptive numerical solution of MFS systems, in The Method of Fundamental Solutions - A Meshless Method,
eds. C.S. Chen, A. Karageorghis, Y.S. Smyrlis, Dynamic Publishers, 2008, p. 1-27. pdf

Limit Problems for Interpolation by Analytic Radial Basis Functions,  pdf file and MAPLE©  worksheet 
Journal of Computational and Applied Mathematics 212,  2008,  127-149, online version

Solvability of Partial Differential Equations by Meshless Kernel Methods  (with Y.C. Hon),
Adv. in Computational Mathematics 28, 2008, 283-299,   new pdf  old pdf

Recovery of Functions From Weak Data Using Unsymmetric Meshless Kernel-Based Methods,
Applied Numerical Mathematics, Volume 58, 2008, 726-741,  pdf file, online version, and MATLAB©  tgz file

Convergence of Unsymmetric Kernel-Based Meshless Collocation Methods,
SIAM J. Numer. Anal. 45/1 (2007), p. 333-351,   pdf 

A Posteriori Error Estimates for Meshless Methods, 
6-page abstract for ECCOMAS 2007, pdf  

Why Does MLPG Work?
Accepted paper for a keynote lecture in ICCES 07, 2006, pdf 

Results on Meshless Collocation Techniques (with L. Ling and R. Opfer),
Engineering Analysis with Boundary Elements, Volume 30, Issue 4, 2006, 247-253  pdf, online version

Kernel-B-Splines and Interpolation (with M. Bozzini and L. Lenarduzzi)  later pdf   older pdf
Numerical Algorithms 41 (2006) p. 1-16          

Kernel Techniques: From Machine Learning to Meshless Methods (with H. Wendland),
Acta Numerica 15, 2006,  p. 543-639,  pdf 

Linearly Constrained Reconstruction  of Functions by Kernels, with Applications to Machine Learning (with J. Werner),
Adv. in Comp. Math. 25 (2006) p. 237-258     pdf

Convergence Analysis of Methods for Solving General Equations,
Proceedings 27th World Conference on Boundary Elements and other Mesh Reduction Methods, 15 - 17 March 2005, Orlando, Florida, USA (BEM05)  pdf 

Multivariate Interpolation by Polynomials and Radial Basis Functions, 
Constructive Approximation 21, p. 293-317, 2005    pdf file 

Near-optimal Data-independent Point Locations for Radial Basis Function Interpolation (with St. de Marchi and H. Wendland), 
Adv. in Comp. Math. 23, 317- 330, 2005,  pdf

On Adaptive Unsymmetric Meshless Collocation (with L. Ling), 
Proceedings of the 2004 International Conference on Computational & Experimental Engineering and Sciences (Forsyth, USA) (S.N. Atluri and A.J.B. Tadeu, eds.), 
CD-ROM, Advances in Computational & Experimental Engineering & Sciences, Tech Science Press, 2004, paper # 270  pdf

Interpolation by Basis Functions of Different Scales and Shapes (with M. Bozzini, L. Lenarduzzi, M. Rossini),
CALCOLO 41, 77-87 (2004),  pdf

Numerische Mathematik (with H. Wendland), Springer, 5. edition, 2004   link

On the Versatility of Meshless Kernel Methods,
Advances in Computational and Experimental Engineering and Sciences,
eds. S.N. Atluri, D.E. Beskos, D. Polyzos, CD ROM, ICCES proceedings paper #428, 2003  pdf 

Special Techniques for Kernel-Based Reconstruction of Functions from Meshless Data,
International Workshop on Meshfree Methods 2003, Lisbon, extended abstract,  pdf

An Adaptive Greedy Algorithm for Solving Large RBF Collocation Problems (with Y.C. Hon and X. Zhou),
Numerical Algorithms 32 (2003), 13-25, pdf

Mathematical Results Concerning Kernel Techniques,
Proceedings of the 13th IFAC Symposium on System Identification, 2003 pdf

Recent Developments in the Dual Reciprocity Method Using Compactly Supported Radial Basis Functions (with C.S. Chen and M. A. Golberg),  in:
Transformation of Domain Effects to the Boundary, ed. Y.F. Rashed and C.A. Brebbia,, 2003,
Advances in Boundary Elements 14,WIT Press, Southampton, Boston, 138-225, pdf

Approximation by Positive Definite Kernels (with H. Wendland), in: Advanced Problems in Constructive Approximation
(M.D. Buhmann and D.H. Mache, eds.), International Series in Numerical Mathematics 142 (2002) 203-221  pdf

Stability of Radial Basis Function Interpolants, Approximation Theory X: Wavelets, Splines, and Applications (C.K. Chui, L.L. Schumaker, and J. Stöckler, eds.)
Vanderbilt Univ. Press, Nashville 2002, p. 433-440  pdf

Inverse and saturation theorems for radial basis function interpolation (with H. Wendlland),  Mathematics of Computation 71 (2002), 669-681 early pdf   later pdf

Adaptive Interpolation by Scaled Multiquadrics (with M. Bozzini and  L. Lenarduzzi), Adv. in Comp. Math.16 (2002), 375-387  ps

Approximation in Sobolev Spaces by Kernel Expansions (with F.J. Narcowich and J.D. Ward), J. of Approx. Th. 114 (2002) 70-83   pdf

Optimal Stability Results for Interpolation by Kernel Functions  (with F.J. Narcowich and J.D. Ward), preprint 2001  pdf

Characterization and Construction of Radial Basis Functions (with H. Wendland),
in: Multivariate Approximation and Applications (N. Dyn, D. Leviatan, D. Levin, and A. Pinkus, eds.),
Cambridge University Press, 2001, p.1-24  pdf

Adaptive greedy techniques for approximate solution of large rbf systems  (with H. Wendland) , Numerical Algorithms 24 (2000), 239-254   earlier pdf     pdf

Remarks on Meshless Local Construction of Surfaces, invited survey, The mathematics of surfaces IX  (eds: R. Cipolla et. al. )
Proceedings of the Ninth IMA Conference on the Mathematics of Surfaces , Springer,  2000 pdf

Numerical Techniques Based on Radial Basis Functions (with H. Wendland),
in:  Curve and Surface Fitting: Saint-Malo 1999 (invited lecture) , Albert Cohen, Christophe Rabut, and Larry L. Schumaker (eds.), Vanderbilt University Press,  2000,  p. 359-374  pdf

A Unified Theory of Radial Basis Functions (Native Hilbert Spaces for Radial Basis Functions II),
J. of Computational and Applied Mathematics 121 (2000) 165--177   pdf

On Unsymmetric Collocation by Radial Basis Functions (with. Y.C. Hon),
Journal of Applied Mathematics and Computation 119,  177-186, 2001   pdf

Using compactly supported radial basis functions to solve partial differential equations (with H. Wendland),
in Boundary Element Technology XIII (invited lecture) , Chen, C. S. and Brebbia, C. A.  and Pepper, D. W. (eds), WitPress, Southampton, Boston, 1999, 311--324   pdf  

Native Hilbert Spaces for Radial Basis Functions I,
International Series of Numerical Mathematics 132 (1999), Birkhäuser Verlag, 255-282,
--->  pdf file (71 Kb)

Multilevel Interpolation and Approximation   (with F. Narcowich & J. Ward, Texas A&M University),
Appl. Comput. Harmonic Anal., 7 (1999) 243-261  pdf

Mathematical model of a LIF-fibre optic sensor head for trace detection in soil
(with U. Bünting, F. Lewitzka, and P. Karlitschek),
Applied Spectroscopy 53 ,49-56 (1999)

Improved Error Bounds for Scattered Data Interpolation by Radial Basis Functions,
Math. Comp. 68 (1999), 201-216  ---> pdf

Optimal Geometric Hermite Interpolation of Curves,
in: Mathematical methods for curves and surfaces II,
Innov. Appl. Math. p. 417-428, Vanderbilt U. Press, Nashville TN, 1998  pdf

Convergence Order Estimates of Meshless Collocation Methods using Radial Basis Functions (with C. Franke),
Advances in Computational Mathematics, Volume 8, Issue 4, June 1998, pp. 381-399 --->  pdf 

Grundlagen der Informatik für das Nebenfachstudium, Vieweg, 1998

Solving Partial Differential Equations by Collocation using Radial Basis Functions (with C. Franke),
Applied Mathematics and Computation, Volume 93, Issue 1, June 1998, pp. 73-82
---> abstractgezipped ps file (82 Kb)

Radial Basis Functions Viewed from Cubic Splines,
in: Multivariate Approximation and Splines, G. Nürnberger, J.W. Schmidt, and G. Walz (eds.),
Birkhäuser 1997, pp. 245-258   --->   pdf

Construction Techniques for Highly Accurate Quasi-Interpolation Operators (with Z. Wu),
J. of Approx. Th. 91 (1997) pp. 320-331   --->  abstractgzipped ps file (48 Kb)

Optimal Recovery of Functions in Translation-invariant Spaces of Functions,
Annals of Numerical Mathematics 4 (1997) pp. 547-555   ---> abstractgzipped ps file (40 Kb)

On the Efficiency of Interpolation by Radial Basis Functions,
in: A. LeMéhauté, C. Rabut, and L.L Schumaker (eds.):
Proceedings of Chamonix 1996, pp. 309-318   --->  abstractgzipped ps file (45 Kb)

Multivariate Interpolation and Approximation by Translates of a Basis Function,
Approximation Theory VIII (invited lecture), C.K. Chui , L.L. Schumaker (eds),
Vanderbilt University Press 1996, 25 pages, survey   ---> abstractgezipped ps file (74 Kb)  pdf file (85 Kb)

Operators on radial functions (with Z. Wu),
J. of Computational and Appl. Math. 73 (1996) pp. 257-270   --->  pdf file 

Approximation by Radial Basis Functions with Finitely Many Centers,
Constructive Approximation 12 (1996) pp. 331-340   ---> pdf file (51 Kb)

Error Estimates and Condition Numbers for Radial Basis Function Interpolation,
Advances in Computational Mathematics 3 (1995) pp. 251-264
  --->  pdf file   pdf file of Table 2

Creating Surfaces from Scattered Data Using Radial Basis Functions,
Mathematical Methods in Computer Aided Geometric Design III,
M. Dæhlen, T. Lyche and L.L. Schumaker (eds.), Vanderbilt Univ. Press, 1995, pp. 477-496
  --->  pdf file 

Lower Bounds for Norms of Inverses of Interpolation Matrices for Radial Basis Functions,
J. of Approx. Th. 79 (1994) pp. 287-306   --->   pdf file 

Reproduction of Polynomials by Radial Basis Functions,
Wavelets, Images, and Surface Fitting, P.J. Laurent, A. LeMéhauté, and L.L. Schumaker (eds.),
AKPeters, 1994, pp. 459-466   --->  pdf file 

Limits of Bernstein-Bézier Curves for Periodic Control Nets (with Dong-Xu Qi),
J. of Approximation Theory and Applications 10 (1994) pp. 5-16   --->  pdf file 

Shape preserving properties and convergence of univariate multiquadric quasi-interpolation (with Z. Wu),
Acta Math. Appl. Sin., Engl. Ser. 10, No. 4, pp. 441-446 (1994)
  --->   pdf file 

Local Error Estimates for Radial Basis Function Interpolation of Scattered Data (with Z. Wu),
IMA J. Numer. Anal. 13 (1993) pp. 13-27   --->   pdf file 

Comparison of Radial Basis Function Interpolants,
in K. Jetter, L.L. Schumaker and F. Utreras (eds.):
``Multivariate Approximations: From CAGD to Wavelets'',
World Scientific, 1993, pp. 293-305   --->  pdf

Planar Curve Interpolation by Piecewise Conics of Arbitrary Type,
Constr. Approx. 9, 1993, pp. 373-389   --->  pdf 

Error Estimates for Approximations from Control Nets,
CAGD 10, 1993, pp. 57-66   --->  pdf 

A Parallel Multistage Method for Surface-Surface Intersection (with H. Bürger)
in R.E. Barnhill, W. Boehm, and J. Hoschek (eds.):
Freiformkurven und -flächen, Proceedings of an Oberwolfach conference,
CAGD 10, 1993, pp. 277-291   --->  pdf  file 1   pdf file 2 

A Multi-Parameter Method for Nonlinear Least-Squares Approximation,
in D. Braess and L.L Schumaker (eds.): Numerical Methods of Approximation Theory 9,
ISNM 105, Birkhäuser, 1992, pp. 269-283   ---> pdf  

Rational Geometric Curve Interpolation,
in T. Lyche and L.L. Schumaker (eds.):
``Mathematical Methods in Computer Aided Geometric Design II'',
Academic Press, 1992, pp. 517-535, survey   ---> pdf 

Numerische Mathematik (with H. Werner),
4. edition, completely rewritten and in one volume,
Springer Verlag, 1992, 326 pages   

Geometrical differentiation and high-accuracy curve interpolation,
in S.P. Singh (ed.): Approximation Theory, Spline Functions, and Applications,
NATO ASI Series C, Vol. 356, Kluwer, 1992, pp. 445-462   --->  pdf  

An Extended Continuous Newton Method (with I. Diener),
Journal of Optimization Theory and Applications 67, 1990, pp. 87-107  --->   pdf

Remarks on High Accuracy Planar Curve Interpolation,
short preprint 1990, not submitted   --->  pdf

Adaptive Rational Splines,
Constructive Approximation 6, 1990, pp. 167-179   --->  pdf

Interpolation in IR2 by piecewise quadratic visually C2 Bézier polynomials,
Computer Aided Geometric Design 6, 1989, pp. 219-233   --->  pdf 

Convergence of Planar Curve Interpolation Schemes,
in C.K. Chui, L.L. Schumaker and J.D. Ward (eds): Approximation Theory VI, 1989, pp. 581-584
  --->    pdf

On Global GC2 Convexity Preserving Interpolation of Planar Curves by Piecewise Bézier Polynomials,
in T. Lyche and L.L. Schumaker (eds.): Mathematical Methods in Computer Aided Geometric Design,
Academic Press 1989, 539-547   --->    pdf

On the expected sublinearity of the Boyer-Moore algorithm,
SIAM J. of Computing 17, 1988, pp. 648-658   link    pdf

Convergence theorems for nonlinear approximation algorithms.
Numerical methods of approximation theory, Vol. 8 (Oberwolfach, 1986), 188–200,
Internat. Schriftenreihe Numer. Math., 81, Birkhäuser, Basel, 1987. 65D15

Helmut Werner (with D. Braess). (German) Jahresber. Deutsch. Math.-Verein. 89 (1987), no. 4, 179–195

Numerische Approximation. [Numerical approximation] Jahresber. Deutsch. Math.-Verein. 88 (1986), no. 2, 51–81

Interaktive graphische Simulation kontinuierlicher Systeme:
Die Benutzerschnittstelle des Systems IMP,
in: D.P.F. Müller (ed.) Simulationstechnik, vol. 109, p. 215-219, Springer 1985

Convergence analysis of the general Gauss-Newton algorithm. Numer. Math. 46 (1985), no. 2, 281–309. Link

An interactive system for simulation and graphic evaluation of discrete and continuous systems (with J. Krauth),
in: W. Ameling(ed.), First European Simulation Congress 1983, vol. 71 of Informatik-Fachberichte, p. 234-238, Springer, 1983

Ein interaktives System zur Simulation, Parameterschätzung und graphischen Auswertung diskreter und kontinuierlicher Modelle,
in: M. Goller (ed.) Simulationstechnik, vol. 56, p. 166-172, Springer 1982

Fehlerabschätzungen für Koeffizienten von Exponentialsummen und Polynomen.
[Error estimates for coefficients of exponential sums and polynomials]
Numer. Math. 39 (1982), no. 2, 293–307 Link

Optimal nodes for interpolation in Hardy spaces. Math. Z. 179 (1982), no. 2, 169–178 Link

Numerical error evaluation in linear approximation—the least-squares case.
in: Approximation theory, III (Proc. Conf., Univ. Texas, Austin, Tex., 1980), pp. 791–798,
Academic Press, New York-London, 1980

Bemerkungen zur Fehlerabschätzung bei linearer Tschebyscheff-Approximation.
In: Numerical methods of approximation theory, Vol. 5 (Conf., Math. Res. Inst., Oberwolfach, 1979), pp. 255–276,
Internat. Ser. Numer. Math., 52, Birkhäuser, Basel-Boston, Mass., 1980

Suboptimal exponential approximations. SIAM J. Numer. Anal. 16 (1979), no. 6, 1007–1018 Link

Praktische Mathematik. II (with Helmut Werner). Second, revised and enlarged edition.
Hochschultext. Springer-Verlag, Berlin-New York, 1979. viii+388 pp. ISBN: 3-540-09193-9 65-01

Eine rundungsgenaue Formel zur maschinellen Berechnung der Prager-Oettli-Schranke. Computing 20 (1978), no. 2, 177–182. Link

On alternation numbers in nonlinear Chebyshev approximation. J. Approx. Theory 23 (1978), no. 4, 379–391 Link

Die numerische Berechnung von Startnäherungen bei der Exponentialapproximation (with H. Robitzsch),
in: Numerische Methoden der Approximationstheorie,
Band 4 (Meeting, Math. Forschungsinst., Oberwolfach, 1977), pp. 260–280,
Internat. Schriftenreihe Numer. Math., 42, Birkhäuser, Basel-Boston, Mass., 1978.

Die Beiträge von Carl-Friedrich Gauß zur Numerischen Mathematik, Lecture 1977,  pdf

Globale Konvergenz von Verfahren zur nichtlinearen Approximation,
in: Approximation theory (Proc. Internat. Colloq., Inst. Angew. Math., Univ. Bonn, Bonn, 1976), pp. 352–363. Springer, Berlin, 1976.

Calculation of best approximations by rational splines,
in: Approximation theory, II (Proc. Internat. Sympos., Univ. Texas, Austin, Tex., 1976), pp. 533–539. Academic Press, New York, 1976.

Finite Elemente. (with J. Frehse and R. Leis). Tagungsband des Sonderforschungsbereiches 72.
Bonner Mathematische Schriften, No. 89. Institut für Angewandte Mathematik, Universität Bonn, Bonn, 1976. ii+121 pp. 65-06

Approximation Theory (with K. Scherer), vol. 556 of Lecture Notes in Mathematics, Springer 1976

Ein Optimierungsproblem aus der Kristallographie,
in: Numerische Methoden bei Optimierungsaufgaben, Band 2 (Tagung, Math. Forschungsinst., Oberwolfach, 1973), pp. 113–123
Internat. Schriftenreihe Numer. Math., Band 23, Birkhäuser, Basel, 1974

Konstruktion von Spline-Interpolierenden und Peano-Kernen,
in: Spline-Funktionen (Tagung, Math. Forschungsinst., Oberwolfach, 1973), pp. 243–255,
Bibliographisches Inst., Mannheim, 1974

Eine Bibliographie zur nichtlinearen Approximationstheorie (with D. Braess and J. Brink-Spalink),
Schriftenreihe des Sonderforschungsbereiches 72, Universität Bonn, Bonn, 1974. i+34 pp. 41-XX

Kollokation mit mehrdimensionalen Spline-Funktionen.
in: Numerische Behandlung nichtlinearer Integrodifferential- und Differentialgleichungen (Tagung, Math. Forschungsinst., Oberwolfach, 1973),
pp. 291–300. Lecture Notes in Math., Vol. 395, Springer, Berlin, 1974

Konstruktion und algebraische Eigenschaften von M-Spline-Interpolierenden. (German) Numer. Math. 21 (1973/74), 166–180. Link

Optimale Interpolations- und Approximationssysteme. (German) Math. Z. 130 (1973), 339–349 Link

Interpolation mit nichtlinearen Klassen von Spline-Funktionen. J. Approximation Theory 8 (1973), 173–188

Spezielle rationale Splinefunktionen, J. Approximation Theory 7 (1973), 281–292

Praktische Mathematik. II: Methoden der Analysis with H. Werner) Hochschultext. Springer-Verlag, Berlin-New York, 1972. vi+355 pp

Anwendungen der konvexen Optimierung auf Approximationstheorie und Splinefunktionen, in:
Methoden und Verfahren der mathematischen Physik, Band 6, pp. 129–151. B. I.-Hochschultaschenbücher, No. 725, Bibliographisches Inst., Mannheim, 1972

Praktische Mathematik. I: Methoden der linearen Algebra. (with H. Werner)
Vorlesung gehalten im Wintersemester 1968/69. Nach einem von R. Schaback angefertigten Skriptum, herausgegeben mit Unterstützung von R. Runge und U. Ebert.
Mathematica Scripta, 1 Springer-Verlag, Berlin-New York 1970 x+275 pp.

Eine Lösungsmethode für die lineare Tschebyscheff-Approximation bei nicht erfüllter Haarscher Bedingung with D. Braess)  Computing (Arch. Elektron. Rechnen) 6,  1970