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Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]]
| Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]] |
| Autore | Buhmann M. D (Martin Dietrich), <1963-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2003 |
| Descrizione fisica | 1 online resource (x, 259 pages) : digital, PDF file(s) |
| Disciplina | 511/.42 |
| Collana | Cambridge monographs on applied and computational mathematics |
| Soggetto topico | Radial basis functions |
| ISBN |
1-107-12800-5
1-280-43229-2 9786610432295 0-511-17904-9 0-511-04020-2 0-511-14894-1 0-511-32602-5 0-511-54324-7 0-511-05124-7 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. 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. |
| Record Nr. | UNINA-9910449712003321 |
Buhmann M. D (Martin Dietrich), <1963->
|
||
| Cambridge : , : Cambridge University Press, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]]
| Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]] |
| Autore | Buhmann M. D (Martin Dietrich), <1963-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2003 |
| Descrizione fisica | 1 online resource (x, 259 pages) : digital, PDF file(s) |
| Disciplina | 511/.42 |
| Collana | Cambridge monographs on applied and computational mathematics |
| Soggetto topico | Radial basis functions |
| ISBN |
1-107-12800-5
1-280-43229-2 9786610432295 0-511-17904-9 0-511-04020-2 0-511-14894-1 0-511-32602-5 0-511-54324-7 0-511-05124-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. 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. |
| Record Nr. | UNINA-9910783009603321 |
|
Buhmann M. D (Martin Dietrich), <1963->
|
||
| Cambridge : , : Cambridge University Press, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]]
| Radial basis functions : theory and implementations / / Martin Buhmann [[electronic resource]] |
| Autore | Buhmann M. D (Martin Dietrich), <1963-> |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2003 |
| Descrizione fisica | 1 online resource (x, 259 pages) : digital, PDF file(s) |
| Disciplina | 511/.42 |
| Collana | Cambridge monographs on applied and computational mathematics |
| Soggetto topico | Radial basis functions |
| ISBN |
1-107-12800-5
1-280-43229-2 9786610432295 0-511-17904-9 0-511-04020-2 0-511-14894-1 0-511-32602-5 0-511-54324-7 0-511-05124-7 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1. 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. |
| Record Nr. | UNINA-9910820483603321 |
|
Buhmann M. D (Martin Dietrich), <1963->
|
||
| Cambridge : , : Cambridge University Press, , 2003 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||