Kernel-Based Meshless Methods

[1]  G. Watson.  Bessel Functions. (Scientific Books: A Treatise on the Theory of Bessel Functions) , 1923 .

[2]  Herbert Meschkowski,et al.  Hilbertsche Räume mit Kernfunktion , 1962 .

[3]  George Gasper,et al.  Positive Integrals of Bessel Functions , 1975 .

[4]  Carl de Boor,et al.  A Practical Guide to Splines , 1978, Applied Mathematical Sciences.

[5]  Gene H. Golub,et al.  Matrix computations , 1983 .

[6]  M. Buhmann.  Convergence of Univariate Quasi-Interpolation Using Multiquadrics , 1988 .

[7]  M. Buhmann.  Multivariate cardinal interpolation with radial-basis functions , 1990 .

[8]  Joseph D. Ward,et al.  Norms of Inverses for Matrices Associated with Scattered Data , 1991, Curves and Surfaces.

[9]  F. J. Narcowich,et al.  Norms of inverses and condition numbers for matrices associated with scattered data , 1991 .

[10]  Zongmin Wu,et al.  Hermite-Birkhoff interpolation of scattered data by radial basis functions , 1992, Approximation Theory and its Applications.

[11]  W. Madych,et al.  Bounds on multivariate polynomials and exponential error estimates for multiquadratic interpolation , 1992 .

[12]  Per Christian Hansen,et al.  Analysis of Discrete Ill-Posed Problems by Means of the L-Curve , 1992, SIAM Rev..

[13]  F. J. Narcowich,et al.  Norm estimates for the inverse of a general class of scattered-data radial-function interpolation matrices , 1992 .

[14]  Dianne P. O'Leary,et al.  The Use of the L-Curve in the Regularization of Discrete Ill-Posed Problems , 1993, SIAM J. Sci. Comput..

[15]  Nira Dyn,et al.  Image Warping by Radial Basis Functions: Application to Facial Expressions , 1994, CVGIP Graph. Model. Image Process..

[16]  F. J. Narcowich,et al.  Generalized Hermite interpolation via matrix-valued conditionally positive definite functions , 1994 .

[17]  Robert Schaback,et al.  Error estimates and condition numbers for radial basis function interpolation , 1995, Adv. Comput. Math..

[18]  Zongmin Wu,et al.  Compactly supported positive definite radial functions , 1995 .

[19]  Holger Wendland,et al.  Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree , 1995, Adv. Comput. Math..

[20]  V. Maz'ya,et al.  On approximate approximations using Gaussian kernels , 1996 .

[21]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[22]  Richard K. Beatson,et al.  Surface interpolation with radial basis functions for medical imaging , 1997, IEEE Transactions on Medical Imaging.

[23]  Alexander J. Smola,et al.  Learning with kernels , 1998 .

[24]  M. Floater,et al.  Thinning algorithms for scattered data interpolation , 1998 .

[25]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[26]  Jun-yong Noh,et al.  Animated deformations with radial basis functions , 2000, VRST '00.

[27]  Jungho Yoon,et al.  Spectral Approximation Orders of Radial Basis Function Interpolation on the Sobolev Space , 2001, SIAM J. Math. Anal..

[28]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[29]  Holger Wendland,et al.  Approximation by positive definite kernels , 2002 .

[30]  Bengt Fornberg,et al.  Stable Computation of Multiquadric Interpolants for All Values of the Shape Parameter , 2004 .

[31]  T. Driscoll,et al.  Interpolation in the limit of increasingly flat radial basis functions , 2002 .

[32]  B. Fornberg,et al.  Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions , 2003 .

[33]  Patrick Reuter,et al.  Point-based modelling and rendering using radial basis functions , 2003, GRAPHITE '03.

[34]  B. Fornberg,et al.  A numerical study of some radial basis function based solution methods for elliptic PDEs , 2003 .

[35]  Nello Cristianini,et al.  Kernel Methods for Pattern Analysis , 2003, ICTAI.

[36]  Y. Hon,et al.  A MESHLESS SCHEME FOR SOLVING INVERSE PROBLEMS OF LAPLACE EQUATION , 2003 .

[37]  Hans-Peter Seidel,et al.  A multi-scale approach to 3D scattered data interpolation with compactly supported basis functions , 2003, 2003 Shape Modeling International..

[38]  Niu Bao-guo.  Solving the Inverse Problem of Determining the Boundary of a Parabolic Equation by Radial Basis Method , 2004 .

[39]  Jichun Li,et al.  Application of radial basis meshless methods to direct and inverse biharmonic boundary value problems , 2004 .

[40]  Holger Wendland,et al.  Scattered Data Approximation: Conditionally positive definite functions , 2004 .

[41]  Jichun Li,et al.  A radial basis meshless method for solving inverse boundary value problems , 2004 .

[42]  G. Fasshauer.  RBF Collocation Methods As PseudospectralMethods , 2005 .

[43]  Holger Wendland,et al.  Approximate Interpolation with Applications to Selecting Smoothing Parameters , 2005, Numerische Mathematik.

[44]  A. Cheng,et al.  Direct solution of ill‐posed boundary value problems by radial basis function collocation method , 2005 .

[45]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[46]  Saburou Saitoh.  Applications of Reproducing Kernels to Best Approximations, Tikhonov Regularizations and Inverse Problems , 2005 .

[47]  Bangti Jin,et al.  Boundary knot method for some inverse problems associated with the Helmholtz equation , 2005 .

[48]  Leif Kobbelt,et al.  Real‐Time Shape Editing using Radial Basis Functions , 2005, Comput. Graph. Forum.

[49]  Leif Kobbelt,et al.  Efficient spectral watermarking of large meshes with orthogonal basis functions , 2005, The Visual Computer.

[50]  R. Schaback.  Convergence Analysis Of Methods For SolvingGeneral Equations , 2005 .

[51]  Y. Hon,et al.  The method of fundamental solution for solving multidimensional inverse heat conduction problems , 2005 .

[52]  Nira Dyn,et al.  Adaptive Thinning for Terrain Modelling and Image Compression , 2005, Advances in Multiresolution for Geometric Modelling.

[53]  Y. Hon,et al.  Reconstruction of numerical derivatives from scattered noisy data , 2005 .

[54]  Regine Ahrem,et al.  A Meshless Spatial Coupling Scheme for Large-scale Fluid-structure-interaction Problems , 2006 .

[55]  W. R. Madych,et al.  An estimate for multivariate interpolation II , 2006, J. Approx. Theory.

[56]  F. J. Narcowich,et al.  Sobolev Error Estimates and a Bernstein Inequality for Scattered Data Interpolation via Radial Basis Functions , 2006 .

[57]  Holger Wendland,et al.  Kernel techniques: From machine learning to meshless methods , 2006, Acta Numerica.

[58]  Elisabeth Larsson,et al.  A new class of oscillatory radial basis functions , 2006, Comput. Math. Appl..

[59]  Z. Nashed.  Applications of Wavelets and Kernel Methods in Inverse Problems , 2006 .

[60]  Robert Schaback,et al.  Convergence of Unsymmetric Kernel-Based Meshless Collocation Methods , 2007, SIAM J. Numer. Anal..

[61]  Holger Wendland,et al.  Meshless Collocation: Error Estimates with Application to Dynamical Systems , 2007, SIAM J. Numer. Anal..

[62]  Robert Schaback,et al.  Limit problems for interpolation by analytic radial basis functions , 2008 .

[63]  Holger Wendland,et al.  Approximating the basin of attraction of time-periodic ODEs by meshless collocation , 2009 .

[64]  Martin D. Buhmann,et al.  Radial Basis Functions: Theory and Implementations: Preface , 2003 .

[65]  Christian Rieger,et al.  F ¨ Ur Mathematik in Den Naturwissenschaften Leipzig Sampling Inequalities for Infinitely Smooth Functions, with Applications to Interpolation and Machine Learning Sampling Inequalities for Infinitely Smooth Functions, with Applications to Interpolation and Machine Learning , 2022 .

[66]  Robert Schaback,et al.  Unsymmetric meshless methods for operator equations , 2010, Numerische Mathematik.