Overview

This book presents Complex Harmonic Splines (CHS), which gives an approximation to the Complex Harmonic Function (CHF), in particular the conformal mapping with high accuracy from the unit disc to a domain with arbitrary shape. The volume develops various periodic quasi-wavelets which can be used to solve the Helmholtz integral equation under some boundary conditions with complexity O(N). The last part of the work introduces a class of periodic wavelets with various properties. Audience: This volume will be of interest to applied mathematicians, physicists and engineers whose work involves approximations and expansions, integral equations, functions of a complex variable and numerical analysis.

Full Product Details

Author:   Han-lin Chen
Publisher:   Springer
Imprint:   Springer
Edition:   2000 ed.
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.160kg
ISBN:  

9780792361374

ISBN 10:   0792361377
Pages:   226
Publication Date:   31 January 2000
Audience:   College/higher education ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Theory and Application of Complex Harmonic Spline Functions.- §1.1 The Interpolating Complex Spline Functions on ?.- §1.2 Quasi-Interpolant Complex Splines on ?.- §1.3 Complex Harmonic Splines and Their Function-theoretical Properties.- §1.4 Geometric Property of CHSF.- §1.5 Application of CHSF to Approximation of Conformal Mappings.- §1.6 Algorithm for Computing P(z).- §1.7 The Mappings Between Two Arbitrary Domains.- 2. Periodic Quasi-Wavelets.- §2.1 Periodic Orthonormal Quasi-wavelets.- §2.2 Quasi-wavelets on the Unit Circle.- §2.3 Anti-periodic Orthonormal Quasi-wavelets.- §2.4 Real Valued Periodic Quasi-wavelets.- §2.5 Other Methods in Periodic Multi-resolution Analysis.- 3. The Application of Quasi-Wavelets in Solving a Boundary Integral Equation of the Second Kind.- §3.1 Discretization.- §3.2 Simplifying the Procedure by Using PQW.- §3.3 Algorithm.- §3.4 Complexity.- §3.5 The Convergence of the Approximate Solution.- §3.6 Error Analysis.- §3.7 The Dirichlet Problem.- 4. The Periodic Cardinal Interpolatory Wavelets.- §4.1 The Periodic Cardinal Interpolatory Scaling Functions.- §4.2 The Periodic Cardinal Interpolatory Wavelets.- §4.3 Symmetry of Scaling Functions and Wavelets.- §4.4 Dual Scaling Functions and Dual Wavelets.- §4.5 Algorithms.- §4.6 Localization of PISF via Spline Approach.- §4.7 Localization of PISF via Circular Approach.- §4.8 Local Properties of PCIW.- §4.9 Examples.- Concluding Remarks.- References.- Author Index.

Reviews

'...this book is a rigorous presentation of the numerous interesting mathematical properties and physical applications of complex harmonic spline functions, which is suitable not only as a reference source but also as a textbook for a special topics course or seminar. We are delighted to see the publication of this book and hope that it will foster new research and applications of complex harmonic splines and wavelets. We enthusiasticalloy recommend it to the mathematics and engineering communities.' Journal of Approximation Theory, 106 (2000)

...this book is a rigorous presentation of the numerous interesting mathematical properties and physical applications of complex harmonic spline functions, which is suitable not only as a reference source but also as a textbook for a special topics course or seminar. We are delighted to see the publication of this book and hope that it will foster new research and applications of complex harmonic splines and wavelets. We enthusiasticalloy recommend it to the mathematics and engineering communities.' Journal of Approximation Theory, 106 (2000)

`...this book is a rigorous presentation of the numerous interesting mathematical properties and physical applications of complex harmonic spline functions, which is suitable not only as a reference source but also as a textbook for a special topics course or seminar. We are delighted to see the publication of this book and hope that it will foster new research and applications of complex harmonic splines and wavelets. We enthusiasticalloy recommend it to the mathematics and engineering communities.' Journal of Approximation Theory, 106 (2000)

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