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Multivariate polysplines : applications to numerical and wavelet analysis

Author: Ognyan Kounchev
Publisher: San Diego, Calif. : Academic Press, ©2001.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
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),  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Kounchev, Ognyan.
Multivariate polysplines.
San Diego, Calif. : Academic Press, ©2001
(DLC) 2001089852
(OCoLC)47682190
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ognyan Kounchev
ISBN: 9780124224902 0124224903 9780080525006 0080525008
OCLC Number: 162574536
Description: 1 online resource (xiv, 498 pages) : illustrations
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.
Responsibility: Ognyan Kounchev.
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Abstract:

Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. This book develops the theory of  Read more...

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