Handbook on Analytic-Computational Methods in Applied Mathematics / Edition 1

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Working computationally in applied mathematics is the very essence of dealing with real-world problems in science and engineering. Approxima tion theory-on the borderline between pure and applied mathematics- ha s always supplied some of the most innovative ideas, computational met hods, and original approaches to many types of problems. The first of its kind, the Handbook on Analytic-Computational Methods in Applied M athematics comprises 22 self-contained chapters focused on various asp ects of analytic computational methods in approximation theory and oth er related fields. The articles represent the leading research activit ies of contemporary, mainstream applied mathematics and address proble ms in a broad range of disciplines, from economics to statistics, dyna mic programming, and engineering.

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Editorial Reviews

In 22 long survey and expository articles, scholars of mathematics and fields in which mathematics is used, including statistics, economics, and communications, on methods for working computationally in applied mathematics. They discuss such topics as approximation related to order statistics, inverse problems, inequalities for trapezoidal and midpoint rules, numerical methods for solving equations in Banach spaces, computational harmonic analysis, fast trigonometric transform methods, wavelet methods, classical inequalities, optimality in approximation theory, approximation methods in random and fuzzy environments, global smoothness methods in approximation theory, orthogonal polynomials, digitized partial differential equation methods, quadrature formulations applications, mathematical finance methods, optimization, the connection of Bernstein approximations to real-life sciences, and applications of splines. They are appropriate for researchers and graduate students. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781584881353
  • Publisher: Taylor & Francis
  • Publication date: 6/27/2000
  • Edition number: 1
  • Pages: 1048
  • Product dimensions: 6.50 (w) x 9.60 (h) x 2.18 (d)

Table of Contents

Degree of Approximation of Order Statistics Functionals, Dependent Case, G.A. Anastassiou
Regularization and Stabilization of Inverse Problems, C.W. Groetsch
Trapezoidal Type Rules from an Inequalities Point of View, P. Cerone and S.S. Dragomir
Midpoint Type Rules from an Inequalities Point of View, P. Cerone and S.S. Dragomir
A Unified Approach for Solving Equations, Part I: On Infinite Dimensional Spaces, I.K. Argyros
A Unified Approach for Solving Equations, Part II: On Finite Dimensional Spaces, I.K. Argyros
Uniqueness for Spherically Convergent Multiple Trigonometric Series, J.M. Ash
Roundoff Error Analysis for Fast Trigonometric Transforms, M. Tasche anfd H. Zeuner
Biorthogonal Local Trigonometric Bases, K. Bittner
PĆ³lya-Type Inequalities, C.E. Pearce, J. Pecaric, and S. Varosanec
Limit Theorems and Best Constants in Approximation Theory. Approximation Theory in Random Setting, M.I. Ganzburg
Approximation Theory in Fuzzy Setting, S.G. Gal
Global Smoothness Preservation by Multivariate Bernstein-Type Operators, J. de la Cal and A.M. Valle
Summation Kernels for Orthogonal Polynomial Systems, F. Filbir, R. Lasser, and J. Obermaier
Digitized PDE Method for Data Restoration, S. Osher and J. Shen
Boundary Quadrature Formulas and Their Application, T.-X. He
Value at Risk: Recent Advances, I.M. Khindanova and S. Rachev
Asset and Liability Management: Recent Advances, S. Rachev and Y. Tokat
Optimization Problems in Fair Division Theory, M. Dall'Aglio
Binomial-Type Coefficients and Classical Approximation Processes, M. Campiti
On Scattered Data Representations Using Bivariate Splines, D. Hong

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