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  • 1
    Online Resource
    Online Resource
    Multivariate polysplines : applications to numerical and wavelet analysis (2001)
    San Diego, Calif. :Academic Press,
    Details
    UID:
    almafu_9958063393102883
    Format: 1 online resource (513 p.)
    ISBN: 1-281-02334-5 , 9786611023348 , 0-08-052500-8
    Content: 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 effecti
    Note: Description based upon print version of record. , Front Cover; Multivariate Polysplines: Applications to Numerical and Wavelet Analysis; Copyright Page; Contents; Preface; Chapter 1. Introduction; 1.1 Organization of material; 1.2 Audience; 1.3 Statements; 1.4 Acknowledgements; 1.5 The polyharmonic paradigm; Part I: Introduction to polysplines; Chapter 2. One-dimensional linear and cubic splines; 2.1 Cubic splines; 2.2 Linear splines; 2.3 Variational (Holladay) property of the odd-degree splines; 2.4 Existence and uniqueness of odd-degree splines; 2.5 The Holladay theorem; Chapter 3. The two-dimensional case: data and smoothness concepts , 3.1 The data concept in two dimensions according to the polyharmonic paradigm3.2 The smoothness concept according to the polyharmonic paradigm; Chapter 4. The objects concept: harmonic and polyharmonic functions in rectangular domains in R2; 4.1 Harmonic functions in strips or rectangles; 4.2 "Parametrization" of the space of periodic harmonic functions in the strip: the Dirichlet problem; 4.3 "Parametrization" of the space of periodic polyharmonic functions in the strip: the Dirichlet problem; 4.4 Nonperiodicity in y; Chapter 5. Polysplines on strips in R2 , 5.1 Periodic harmonic polysplines on strips, p =5.2 Periodic biharmonic polysplines on strips, p =; 5.3 Computing the biharmonic polysplines on strips; 5.4 Uniqueness of the interpolation polysplines; Chapter 6. Application of polysplines to magnetism and CAGD; 6.1 Smoothing airborne magnetic field data; 6.2 Applications to computer-aided geometric design; 6.3 Conclusions; Chapter 7. The objects concept: harmonic and polyharmonic functions in annuli in R2; 7.1 Harmonic functions in spherical (circular) domains; 7.2 Biharmonic and polyharmonic functions , 7.3 "Parametrization" of the space of polyharmonic functions in the annulus and ball: the Dirichlet problemChapter 8. Polysplines on annuli in R2; 8.1 The biharmonic polysplines, p = 2; 8.2 Radially symmetric interpolation polysplines; 8.3 Computing the polysplines for general (nonconstant) data; 8.4 The uniqueness of interpolation polysplines on annuli; 8.5 The change v = log r and the operators Mk,p; 8.6 The fundamental set of solutions for the operator Mk,p(d/dv); Chapter 9. Polysplines on strips and annuli in Rn; 9.1 Polysplines on strips in Rn; 9.2 Polysplines on annuli in Rn , 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 , 10.12 Zonal harmonics Z (k) θ' (θ): the functional approach , English
    Additional Edition: ISBN 0-12-422490-3
    Language: English
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    HU Berlin
    FU Berlin
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  • 2
    Online Resource
    Online Resource
    Multivariate polysplines : applications to numerical and wavelet analysis (2001)
    San Diego, Calif. [u.a.] : Academic Press
    Details
    UID:
    gbv_1645862682
    Format: Online Ressource (xiv, 498 p.) , Ill., graph. Darst.
    Edition: Online-Ausg. Amsterdam Elsevier Science & Technology Online-Ressource ScienceDirect
    ISBN: 9780124224902 , 0124224903 , 9780080525006 , 0080525008
    Content: Front Cover; Multivariate Polysplines: Applications to Numerical and Wavelet Analysis; Copyright Page; Contents; Preface; Chapter 1. Introduction; 1.1 Organization of material; 1.2 Audience; 1.3 Statements; 1.4 Acknowledgements; 1.5 The polyharmonic paradigm; Part I: Introduction to polysplines; Chapter 2. One-dimensional linear and cubic splines; Chapter 3. The two-dimensional case: data and smoothness concepts; Chapter 4. The objects concept: harmonic and polyharmonic functions in rectangular domains in R2; Chapter 5. Polysplines on strips in R2
    Content: 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
    Note: Includes bibliographical references (p. 487-490) and index. - Description based on print version record
    Additional Edition: ISBN 0124224903
    Additional Edition: Erscheint auch als Druck-Ausgabe Kunčev, Ognjan I. Multivariate polysplines San Diego, Calif. [u.a.] : Academic Press, 2001 ISBN 0124224903
    Additional Edition: ISBN 9780124224902
    Language: English
    Subjects: Mathematics
    RVK:
    SK 910
    Keywords: Mehrdimensionale Spline-Funktion ; Spline-Approximation ; Wellenfunktion ; Wavelet ; Electronic books
    DOI: 10.1016/B978-0-12-422490-2.X5000-4
    URL: https://doi.org/10.1016/B978-0-12-422490-2.X5000-4
    URL: Volltext
    URL: Volltext  (Deutschlandweit zugänglich)
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    URL: Inhaltstext
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    Online Access
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    Stabi Berlin
    UB Potsdam
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