Multivariate polysplines: applications to numerical and wavelet analysis
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
San Diego, Calif.
Academic Press
©2001
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| Subjects: | |
| Online Access: | Volltext |
| Item Description: | 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 Includes bibliographical references (pages 487-490) and index |
| Physical Description: | 1 Online-Ressource (xiv, 498 pages) |
| ISBN: | 9780124224902 0124224903 9780080525006 0080525008 |
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| 500 | |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 | ||
| 500 | |a Includes bibliographical references (pages 487-490) and index | ||
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 7 | |a Differential equations, Elliptic / Numerical solutions |2 fast | |
| 650 | 7 | |a Polyharmonic functions |2 fast | |
| 650 | 7 | |a Spline theory |2 fast | |
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| 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 | |
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| dewey-tens | 510 - Mathematics |
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| isbn | 9780124224902 0124224903 9780080525006 0080525008 |
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| spelling | Kounchev, Ognyan Verfasser aut Multivariate polysplines applications to numerical and wavelet analysis Ognyan Kounchev San Diego, Calif. Academic Press ©2001 1 Online-Ressource (xiv, 498 pages) txt rdacontent c rdamedia cr rdacarrier 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 Includes bibliographical references (pages 487-490) and index MATHEMATICS / General bisacsh Differential equations, Elliptic / Numerical solutions fast Polyharmonic functions fast Spline theory fast PARTIAL DIFFERENTIAL EQUATIONS. nasat ANALYSIS (MATHEMATICS) nasat MATHEMATICAL MODELS. nasat WAVELET ANALYSIS. nasat APPLICATIONS OF MATHEMATICS. nasat Spline theory Polyharmonic functions Differential equations, Elliptic Numerical solutions Spline (DE-588)4182391-6 gnd rswk-swf Mehrere Variable (DE-588)4277015-4 gnd rswk-swf Spline (DE-588)4182391-6 s Mehrere Variable (DE-588)4277015-4 s 1\p DE-604 http://www.sciencedirect.com/science/book/9780124224902 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kounchev, Ognyan Multivariate polysplines applications to numerical and wavelet analysis MATHEMATICS / General bisacsh Differential equations, Elliptic / Numerical solutions fast Polyharmonic functions fast Spline theory fast PARTIAL DIFFERENTIAL EQUATIONS. nasat ANALYSIS (MATHEMATICS) nasat MATHEMATICAL MODELS. nasat WAVELET ANALYSIS. nasat APPLICATIONS OF MATHEMATICS. nasat Spline theory Polyharmonic functions Differential equations, Elliptic Numerical solutions Spline (DE-588)4182391-6 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| subject_GND | (DE-588)4182391-6 (DE-588)4277015-4 |
| title | Multivariate polysplines applications to numerical and wavelet analysis |
| title_auth | Multivariate polysplines applications to numerical and wavelet analysis |
| title_exact_search | Multivariate polysplines applications to numerical and wavelet analysis |
| title_full | Multivariate polysplines applications to numerical and wavelet analysis Ognyan Kounchev |
| title_fullStr | Multivariate polysplines applications to numerical and wavelet analysis Ognyan Kounchev |
| title_full_unstemmed | Multivariate polysplines applications to numerical and wavelet analysis Ognyan Kounchev |
| title_short | Multivariate polysplines |
| title_sort | multivariate polysplines applications to numerical and wavelet analysis |
| title_sub | applications to numerical and wavelet analysis |
| topic | MATHEMATICS / General bisacsh Differential equations, Elliptic / Numerical solutions fast Polyharmonic functions fast Spline theory fast PARTIAL DIFFERENTIAL EQUATIONS. nasat ANALYSIS (MATHEMATICS) nasat MATHEMATICAL MODELS. nasat WAVELET ANALYSIS. nasat APPLICATIONS OF MATHEMATICS. nasat Spline theory Polyharmonic functions Differential equations, Elliptic Numerical solutions Spline (DE-588)4182391-6 gnd Mehrere Variable (DE-588)4277015-4 gnd |
| topic_facet | MATHEMATICS / General Differential equations, Elliptic / Numerical solutions Polyharmonic functions Spline theory PARTIAL DIFFERENTIAL EQUATIONS. ANALYSIS (MATHEMATICS) MATHEMATICAL MODELS. WAVELET ANALYSIS. APPLICATIONS OF MATHEMATICS. Differential equations, Elliptic Numerical solutions Spline Mehrere Variable |
| url | http://www.sciencedirect.com/science/book/9780124224902 |
| work_keys_str_mv | AT kounchevognyan multivariatepolysplinesapplicationstonumericalandwaveletanalysis |