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Multivariate polysplines : applications to numerical and wavelet analysis /
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
San Diego, Calif. :
Academic Press,
�2001.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kounchev, Ognyan. | |
| 245 | 1 | 0 | |a Multivariate polysplines : |b applications to numerical and wavelet analysis / |c Ognyan Kounchev. |
| 260 | |a San Diego, Calif. : |b Academic Press, |c �2001. | ||
| 300 | |a 1 online resource (xiv, 498 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 520 | |a Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and "smoothing" that are essential in computer aided geometric design (CAGD and CAD/CAM systems), geophysics, magnetism, geodesy, geography, wavelet analysis and signal and image processing. In many cases involving practical data in these areas, polysplines are proving more effective than well-established methods, such as kKriging, radial basis functions, thin plate splines and minimum curvature. Part 1 assumes no special knowledge of partial differential equations and is intended as a graduate level introduction to the topic Part 2 develops the theory of cardinal Polysplines, which is a natural generalization of Schoenberg's beautiful one-dimensional theory of cardinal splines. Part 3 constructs a wavelet analysis using cardinal Polysplines. The results parallel those found by Chui for the one-dimensional case. Part 4 considers the ultimate generalization of Polysplines - on manifolds, for a wide class of higher-order elliptic operators and satisfying a Holladay variational property | ||
| 504 | |a Includes bibliographical references (pages 487-490) and index. | ||
| 505 | 0 | |6 880-01 |a Introduction -- Part I: Introduction to polysplines -- One-dimensional linear and cubic splines -- The two-dimensional case: data and smoothness concepts -- The objects concept: harmonic and polyharmonic functions in rectangular domains in R2 -- Polysplines on strips in R2 -- Application of polysplines to magnetism and CAGD -- The objects concept: Harmonic and polyharmonic functions in annuli in R2 -- Polysplines on annuli in R2 -- Polysplines on strips and annuli in Rn -- Compendium on spherical harmonics and polyharmonics functions -- Appendix on Chebyshev splines -- Appendix on Fourier series and Fourier transform -- Part II: Cardinal polysplines in Rn -- Cardinal L-splines according to Micchelli -- Riesz bounds for the cardinal L-splines QZ+1 -- Cardinal interpolation polysplines on annuli -- Part III: Wavelet analysis -- Chui's cardinal spline wavelet analysis -- Polyharmonic wavelet analysis: Scaling and rationally invariant spaces -- Part IV: Polysplines for general interfaces -- Heuristic arguments -- Definition of polysplines and uniqueness for general interfaces -- A priori estimates and Fredholm operators -- Existence and convergence of polysplines -- Appendix on elliptic boundary value problems in Sobolev and H�older spaces -- Afterword. | |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Spline theory. | |
| 650 | 0 | |a Polyharmonic functions. | |
| 650 | 0 | |a Differential equations, Elliptic |x Numerical solutions. | |
| 650 | 6 | |a Th�eorie des splines. |0 (CaQQLa)201-0063506 | |
| 650 | 6 | |a Fonctions polyharmoniques. |0 (CaQQLa)000270013 | |
| 650 | 6 | |a �Equations diff�erentielles elliptiques |x Solutions num�eriques. |0 (CaQQLa)201-0041234 | |
| 650 | 7 | |a MATHEMATICS |x General. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Elliptic |x Numerical solutions. |2 fast |0 (OCoLC)fst00893461 | |
| 650 | 7 | |a Polyharmonic functions. |2 fast |0 (OCoLC)fst01070510 | |
| 650 | 7 | |a Spline theory. |2 fast |0 (OCoLC)fst01130287 | |
| 650 | 7 | |a PARTIAL DIFFERENTIAL EQUATIONS. |2 nasat | |
| 650 | 7 | |a ANALYSIS (MATHEMATICS) |2 nasat | |
| 650 | 7 | |a MATHEMATICAL MODELS. |2 nasat | |
| 650 | 7 | |a WAVELET ANALYSIS. |2 nasat | |
| 650 | 7 | |a APPLICATIONS OF MATHEMATICS. |2 nasat | |
| 776 | 0 | 8 | |i Print version: |a Kounchev, Ognyan. |t Multivariate polysplines. |d San Diego, Calif. : Academic Press, �2001 |z 0124224903 |z 9780124224902 |w (DLC) 2001089852 |w (OCoLC)47682190 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780124224902 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a Chapter 10. Compendium on spherical harmonics and polyharmonic functions10.1 Introduction; 10.2 Notations; 10.3 Spherical coordinates and the Laplace operator; 10.4 Fourier series and basic properties; 10.5 Finding the point of view; 10.6 Homogeneous polynomials in Rn; 10.7 Gauss representation of homogeneous polynomials; 10.8 Gauss representation: analog to the Taylor series, the polyharmonic paradigm; 10.9 The sets Hk are eigenspaces for the operator Δθ; 10.10 Completeness of the spherical harmonics in L2(Sn-1); 10.11 Solutions of Δw(x) = 0 with separated variables. | |
| 880 | 8 | |6 505-01/(S |a 10.12 Zonal harmonics Z (k) θ' (θ): the functional approach. | |