00000cam a22000003i 4500 UP-1685594773862408812 Buklod 20210419231417.0 m | | ta 210419s1982 riua rb |001 0|eng d 0821813749 9780821813744 (iLib)UPBAG-00039790575 OLC BAG rda eng QA 221 C47 1982 Cheney, E. W. (Elliott Ward) 1929- author. Introduction to approximation theory E.W. Cheney. Approximation theory. Second edition. Providence, Rhode Island AMS Chelsea Publishing [1982] x, 259 pages illustrations 24 cm text rdacontent unmediated rdamedia volume rdacarrier Reprinted by the American Mathematical Society, 1998. Includes bibliographical references (pages 236-254) and index. Introduction: Examples and prospectus -- Metric spaces -- Normed linear spaces -- Inner-product spaces -- Convexity -- Existence and unicity of best approximations -- The Tchebycheff solution of inconsistent linear equations: Introduction -- Systems of equations with one unknown -- Characterization of the solution -- The special case -- Pólya's algorithm -- The ascent algorithm -- The descent algorithm -- Convex programming -- Tchebycheff approximation by polynomials and other linear families: Introduction -- Interpolation -- The Weierstrass theorem -- General linear families -- The unicity problem -- Discretization errors: general theory -- Discretization: algebraic polynomials. The inequalities of Markoff and Bernstein -- Algorithms -- Least-squares approximation and related topics: Introduction -- Orthogonal systems of polynomials -- Convergence of orthogonal expansions -- Approximation by series of Tchebycheff polynomials -- Discrete least-squares approximation -- The Jackson theorems -- Rational approximation: Introduction -- Existence of best rational approximations -- The characterization of best approximations -- Unicity; continuity of best-approximation operators -- Algorithms -- Padé approximation and its generalizations -- Continued fractions -- Some additional topics: The Stone approximation theorem -- The Müntz theorem -- The converses of the Jackson theorems -- Polygonal approximation and bases in -- The Kharshiladze-Lozinski theorems -- Approximation in the mean. Approximation theory. FO UPBAG UPBAG-MAIN QA 221 C47 1982 Book