Wavelets generated by Kernels via Scale Derivatives (with Mira Bozzini,
Milvia Rossini, and Elena Volonte, Milano)
Regularized discrete function reconstruction (with Christian Rieger, Bonn
and Barbara Zwicknagl, Berlin)
Geometric Analysis of Vision Cues for the Flare, 2021, pdf
Modelling Recovered Cases and Death Probabilities for the COVID-19
Outbreak, March 26th, 2020, pdf
arxiv
update of table and figures using data up to April 7: pdf
A Greedy Method for Solving Classes of PDE problems, 2019, pdf
arxiv
The Mathematics of Fuel-to-Distance-Optimal Flight, 2017, arxiv
later
MATLAB Programming for Kernel-Based Methods, technical report 2011, still
not fully revised, pdf
A strongly improved version of the software, by Oleg Davydov, Gießen, is here.
The Matérn Model: A Journey through Statistics, Numerical Analysis and
Machine Learning,
(with Emilio Porcu, Moreno Bevilacqua, and Chris J. Oates),
Statistical Science 39 (2024), 469-492, https://dx.doi.org/10.1214/24-STS923,
arxiv, pdf,
Introducing the evaluation condition number: A novel assessment of
conditioning in radial basis function methods (with A. Noorizadegan),
Engineering Analysis with Boundary Elements 166, 2024, 105827, https://doi.org/10.1016/j.enganabound.2024.105827,
early version:
https://dx.doi.org/10.2139/ssrn.4776821
Scaling of Radial Basis Functions (with Elisabeth Larsson, Uppsala),
IMA Journal of Numerical Analysis 44 (2024), 1130-1152, https://doi.org/10.1093/imanum/drad035,
arxiv
H-Sets for Kernel-Based Spaces, https://doi.org/10.1016/j.jat.2023.105942,
Journal of Approximation Theory 294 (2023), Article 105942, arxiv,
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Small Errors imply Large Evaluation Instabilities, https://doi.org/10.1007/s10444-023-10026-2,
Advances in Computational Mathematics 49, 25 (2023), arxiv,
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An Approximation Theorist's View on Solving Operator Equations, - with
special attention to Trefftz, MFS, MPS, and DRM methods - ,
https://doi.org/10.1016/j.camwa.2019.09.005,
Computers and Mathematics with Applications 88 (2021) 70–77 arxiv
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Convergence Analysis of General Spectral Methods (with Maryam Mohammadi,
Kharazmi University, Tehran, Iran),
Journal of Computational and Applied Mathematics 313, 2017, 284–293, https://doi.org/10.1016/j.cam.2016.09.031,
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Approximation of Eigenfunctions in Kernel-based Spaces (with Gabriele
Santin, Padova),
Advances in Computational Mathematics 42, 2016,
973–993, https://doi.org/10.1007/s10444-015-9449-5,
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All Well--Posed Problems have Uniformly Stable and Convergent
Discretizations,
Numerische Mathematik 132, 2016, 597-630 https://doi.org/10.1007/s00211-015-0731-8,
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Error Bounds for Kernel-Based Numerical Differentiation (with Oleg
Davydov, Univ. Gießen),
Numerische Mathematik 132, 2016, 243-269, https://doi.org/10.1007/s00211-015-0722-9,
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Multivariate Approximation, in: Encyclopedia of Applied and Computational
Mathematics,
ISBN 978-3-540-70528-4, 2015, https://doi.org/10.1007/978-3-540-70529-1_370,
Springer-Verlag Berlin Heidelberg pdf
Shift-Invariant Approximation, in: Encyclopedia of Applied and
Computational Mathematics,
ISBN 978-3-540-70528-4, 2015, https://doi.org/10.1007/978-3-540-70529-1_334,
Springer-Verlag Berlin Heidelberg pdf
Radial Kernels via Scale Derivatives (with M. Bozzini, M. Rossini and E.
Volonte, Univ. Milano-Biccocca),
Adv. in Comp. Math. 41 (2015) 277-291, https://doi.org/10.1007/s10444-014-9366-z,
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A meshless method for solving the 2D Brusselator reaction-diffusion
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Computer Modeling in Engineering & Sciences, Vol. 101, No. 2, pp.
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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, https://doi.org/10.1016/j.camwa.2014.09.015,
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Greedy Sparse Linear Approximations of Functionals from Nodal Data, https://doi.org/10.1007/s11075-013-9806-8,
Numerical Algorithms: Volume 67, Issue 3 (2014), Page 531-547, (with
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Solving Heat Conduction Problems by the Direct Meshless Local
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Numerical Algorithms 65 no. 2, 275-291, 2014, https:/doi.org/10.1007/s11075-013-9711-1,
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Interpolation of spatial data - a stochastic or a deterministic problem?,
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European Journal of Applied Mathematics 24 Nr. 4, 2013, pp. 601-629, https://doi.org/10.1017/S0956792513000016,
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Generalized Whittle--Matern and Polyharmonic Kernels, with Mira
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Direct Discretizations with Applications to Meshless Methods for PDEs,
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Multivariate Interpolation by Polynomials and Radial Basis
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Constructive Approximation 21, p. 293-317, 2005, https://doi.org/10.1007/s00365-004-0585-2,
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Near-optimal Data-independent Point Locations for Radial Basis Function
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Adv. in Comp. Math. 23, 317- 330, 2005, https://doi.org/10.1007/s10444-004-1829-1,
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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
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Interpolation by Basis Functions of Different Scales and Shapes (with M.
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CALCOLO 41, 77-87 (2004), https://doi.org/10.1007/BF02637256,
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On the Versatility of Meshless Kernel Methods,
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eds. S.N. Atluri, D.E. Beskos, D. Polyzos, CD ROM, ICCES proceedings paper
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An Adaptive Greedy Algorithm for Solving Large RBF Collocation Problems
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Numerical Algorithms 32 (2003), 13-25, https://doi.org/10.1023/A:1022253303343,
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Mathematical Results Concerning Kernel Techniques,
Proceedings of the 13th IFAC Symposium on System Identification, 2003
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Recent Developments in the Dual Reciprocity Method Using Compactly
Supported Radial Basis Functions (with C.S. Chen and M. A. Golberg),
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Approximation in Sobolev Spaces by Kernel Expansions (with F.J. Narcowich
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Numerical Techniques Based on Radial Basis Functions (with H. Wendland),
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International Series of Numerical Mathematics 132 (1999), Birkhäuser
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in soil
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Applied Spectroscopy 53 ,49-56 (1999)
Improved Error Bounds for Scattered Data Interpolation by Radial Basis
Functions,
Math. Comp. 68 (1999), 201-216 ---> pdf
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and G. Walz (eds.),
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Operators on radial functions (with Z. Wu),
J. of Computational and Appl. Math. 73 (1996) pp. 257-270
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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
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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
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Lower Bounds for Norms of Inverses of Interpolation Matrices for Radial
Basis Functions,
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Reproduction of Polynomials by Radial Basis Functions,
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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.
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in D. Braess and L.L Schumaker (eds.): Numerical Methods of Approximation
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ISNM 105, Birkhäuser, 1992, pp. 269-283 ---> pdf
Rational Geometric Curve Interpolation,
in T. Lyche and L.L. Schumaker (eds.):
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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
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Journal of Optimization Theory and Applications 67, 1990, pp. 87-107
---> pdf
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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
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Convergence of Planar Curve Interpolation Schemes,
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1989, pp. 581-584
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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
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pdf