Synopses & Reviews
Interpolation and approximation offer important applications in computer science and elsewhere. This intermediate-level survey by a noted authority abounds in useful examples of related subjects and has been praised for its level of clarity and reliance on well-presented and useful examples.
A brief introductory chapter presents helpful definitions and theorems. Subsequent chapters explore interpolation, remainder theory, convergence theorems for interpolatory processes, and some problems of infinite interpolation. Additional topics include uniform and best approximation, least square approximation, Hilbert space, orthogonal polynomials, the theory of closure and completeness, expansion theorems for orthogonal functions, degree of approximation, and approximation of linear functionals. A familiarity with real and complex variable theory and linear algebra is assumed.
Dover (2014) corrected republication of the edition originally published by the Blaisdell Publishing Company, Waltham, Massachusetts, 1963.
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Synopsis
Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.
About the Author
Philip J. Davis is Professor Emeritus of Applied Mathematics at Brown University. His other Dover books include Methods of Numerical Integration: Second Edition, and Descartes' Dream: The World According to Mathematics (co-written with Reuben Hersh).