| Description |
1 online resource (xiv, 498 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 487-490) and index. |
| Contents |
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 Hölder spaces -- Afterword. |
| Note |
Print version record. |
| Subject |
Spline theory.
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Polyharmonic functions.
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Differential equations, Elliptic -- Numerical solutions.
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Théorie des splines.
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Fonctions polyharmoniques.
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Équations différentielles elliptiques -- Solutions numériques.
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MATHEMATICS -- General.
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Differential equations, Elliptic -- Numerical solutions
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Polyharmonic functions
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Spline theory
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PARTIAL DIFFERENTIAL EQUATIONS.
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ANALYSIS (MATHEMATICS)
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MATHEMATICAL MODELS.
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WAVELET ANALYSIS.
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APPLICATIONS OF MATHEMATICS.
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| Other Form: |
Print version: Kounchev, Ognyan. Multivariate polysplines. San Diego, Calif. : Academic Press, ©2001 0124224903 9780124224902 (DLC) 2001089852 (OCoLC)47682190 |
| ISBN |
9780124224902 |
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0124224903 |
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9780080525006 (electronic bk.) |
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0080525008 (electronic bk.) |
| Standard No. |
9780124224902 |
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AU@ 000048130649 |
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CHBIS 005681041 |
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CHVBK 167397486 |
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DEBBG BV036962302 |
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DEBBG BV039830170 |
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DEBSZ 275304639 |
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DEBSZ 422200131 |
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NZ1 12433380 |
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NZ1 15192863 |
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DEBBG BV042317312 |
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AU@ 000059689328 |
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