LEADER 04842nam 22006492 450 001 9910449712003321 005 20151005020621.0 010 $a1-107-12800-5 010 $a1-280-43229-2 010 $a9786610432295 010 $a0-511-17904-9 010 $a0-511-04020-2 010 $a0-511-14894-1 010 $a0-511-32602-5 010 $a0-511-54324-7 010 $a0-511-05124-7 035 $a(CKB)1000000000006601 035 $a(EBL)201637 035 $a(OCoLC)171135378 035 $a(SSID)ssj0000232110 035 $a(PQKBManifestationID)11226067 035 $a(PQKBTitleCode)TC0000232110 035 $a(PQKBWorkID)10210246 035 $a(PQKB)11624477 035 $a(UkCbUP)CR9780511543241 035 $a(MiAaPQ)EBC201637 035 $a(Au-PeEL)EBL201637 035 $a(CaPaEBR)ebr10064306 035 $a(CaONFJC)MIL43229 035 $a(EXLCZ)991000000000006601 100 $a20090505d2003|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aRadial basis functions $etheory and implementations /$fMartin Buhmann$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2003. 215 $a1 online resource (x, 259 pages) $cdigital, PDF file(s) 225 1 $aCambridge monographs on applied and computational mathematics ;$v12 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-10133-6 311 $a0-521-63338-9 320 $aIncludes bibliographical references (p. 246-257) and index. 327 $a1. Introduction -- 1.1 Radial basis functions -- 1.2 Applications -- 1.3 Contents of the book -- 2. Summary of methods and applications -- 2.1 Invertibility of interpolation matrices -- 2.2 Convergence analysis -- 2.3 Interpolation and convergence -- 2.4 Applications to PDEs -- 3. General methods for approximation and interpolation -- 3.1 Polynomial schemes -- 3.2 Piecewise polynomials -- 3.3 General nonpolynomial methods -- 4. Radial basis function approximation on infinite grids -- 4.1 Existence of interpolants -- 4.2 Convergence analysis -- 4.3 Numerical properties of the interpolation linear system -- 4.4 Convergence with respect to parameters in the radial functions -- 5. Radial basis functions on scattered data -- 5.1 Nonsingularity of interpolation matrices -- 5.2 Convergence analysis -- 5.3 Norm estimates and condition numbers of interpolation matrices -- 6. Radial basis functions with compact support -- 6.1 Introduction -- 6.2 Wendland's functions -- 6.3 Another class of radial basis functions with compact support -- 6.4 Convergence -- 6.5 A unified class -- 7. Implementations -- 7.1 Introduction -- 7.2 The BFGP algorithm and the new Krylov method -- 7.3 The fast multipole algorithm -- 7.4 Preconditioning techniques -- 8. Least squares methods -- 8.1 Introduction to least squares -- 8.2 Approximation order results -- 8.3 Discrete least squares -- 8.4 Implementations -- 8.5 Neural network applications -- 9. Wavelet methods with radial basis functions -- 9.1 Introduction to wavelets and prewavelets -- 9.2 Basic definitions and constructions -- 9.3 Multiresolution analysis and refinement -- 9.4 Special constructions -- 10. Further results and open problems -- 10.1 Further results -- 10.2 Open problems -- Appendix: Some essentials on Fourier transforms. 330 $aIn many areas of mathematics, science and engineering, from computer graphics to inverse methods to signal processing, it is necessary to estimate parameters, usually multidimensional, by approximation and interpolation. Radial basis functions are a powerful tool which work well in very general circumstances and so are becoming of widespread use as the limitations of other methods, such as least squares, polynomial interpolation or wavelet-based, become apparent. The author's aim is to give a thorough treatment from both the theoretical and practical implementation viewpoints. For example, he emphasises the many positive features of radial basis functions such as the unique solvability of the interpolation problem, the computation of interpolants, their smoothness and convergence and provides a careful classification of the radial basis functions into types that have different convergence. A comprehensive bibliography rounds off what will prove a very valuable work. 410 0$aCambridge monographs on applied and computational mathematics ;$v12. 606 $aRadial basis functions 615 0$aRadial basis functions. 676 $a511/.42 700 $aBuhmann$b M. D$g(Martin Dietrich),$f1963-$01054403 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910449712003321 996 $aRadial basis functions$92486946 997 $aUNINA