Introduction to Approximation Theory
American Mathematical Society (Verlag)
978-0-8218-1374-4 (ISBN)
Introduction: 1 Examples and prospectus 2 Metric spaces 3 Normed linear spaces 4 Inner-product spaces 5 Convexity 6 Existence and unicity of best approximations 7 Convex functions The Tchebycheff Solution of Inconsistent Linear Equations: 1 Introduction 2 Systems of equations with one unknown 3 Characterization of the solution 4 The special case 5 Polya's algorithm 6 The ascent algorithm 7 The descent algorithm 8 Convex programming Tchebycheff Approximation by Polynomials and Other Linear Families: 1 Introduction 2 Interpolation 3 The Weierstrass theorem 4 General linear families 5 the unicity problem 6 Discretization errors: General theory 7 Discretization: Algebraic polynomials. The inequalities of Markoff and Bernstein 8 Algorithms Least-squares Approximation and Related Topics: 1 Introduction 2 Orthogonal systems of polynomials 3 Convergence of orthogonal expansions 4 Approximation by series of Tchebycheff polynomials 5 Discrete least-squares approximation 6 The Jackson theorems Rational Approximation: 1 Introduction 2 Existence of best rational approximations 3 The characterization of best approximations 4 Unicity; Continuity of best-approximation operators 5 Algorithms 6 Pade Approximation and its generalizations 7 Continued fractions Some Additional Topics: 1 The Stone approximation theorem 2 The Muntz theorem 3 The converses of the Jackson theorems 4 Polygonal approximation and bases in $C[a, b]$ 5 The Kharshiladze-Lozinski theorems 6 Approximation in the mean Notes References Index.
Erscheint lt. Verlag | 1.1.1999 |
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Reihe/Serie | AMS Chelsea Publishing |
Zusatzinfo | notes, references, index |
Verlagsort | Providence |
Sprache | englisch |
Gewicht | 550 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
Mathematik / Informatik ► Mathematik ► Analysis | |
ISBN-10 | 0-8218-1374-9 / 0821813749 |
ISBN-13 | 978-0-8218-1374-4 / 9780821813744 |
Zustand | Neuware |
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