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Constructive Function Theory. Volume III: Interpolation and Approximation Quadratures
Posted on 2010-04-01
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More I. P. Natanson, "" Chapter I. VARIOUS METHODS OF INTERPOLATION 1. The Problem 2 The LAGRANGE Formula 3. A Rearrangement of the LAGRANGE Formula - NEWTON'S Formula 4. Interpolation with Multiple Nodes 5. Trigonometric Interpolation Chapter II. THEOREMS OF NEGATIVE CHARACTER 1. The Theorems of S. N. BERNSTEIN and G. FABER 2. The BERNSTEIN Example 3. An Example Due to MARCINKIEWICZ Chapter III. THE CONVERGENCE OF INTERPOLATION PROCESSES 1. The Role of the Function An(X) 2. The Theorems of GRUNWALD and TURAN 3. Convergence in Mean 4. The FEJER Interpolation Process 5. Generalization of the Preceding Results 6. Normal Matrices Chapter IV. SEVERAL CONVERGENCE PROCESSES RELATED TO INTERPOLATION 1. The First BERNSTEIN Procedure 2. The Second BERNSTEIN Procedure 3. A Theorem of S. M. LOSINSKI and the Method of S.J. RAPPOPORT 4. The Third BERNSTEIN Procedure 5. Certain General Properties of Summation Formulas Chapter V. APPROXIMATION QUADRATURES 1. The Problem 2. The Remainder in the Quadrature Formula 3. Quadratures of Gaussian Type 4. Special Quadratures of Gaussian Type Chapter VI. SUPPLEMENT TO THE THEORY OF APPROXIMATION QUADRATURES 1. The General Quadrature Process and its Convergence 2. Quadratures with Positive Coefficients 3. A Theorem Due to R. O. KUSMIN 4. The TCHEBYSHEFF Problem and a BERNSTEIN Theorem 5. The POSSE Theorem Appendix 1. STIRLING'S FORMULA Appendix 2. ON THE MUNTZ THEOREMS Appendix 3. THE THEOREMS OF S.M. LOSINSKI-F.I. KHARSHILADZE AND V.F. NIKOLAEV Bibliography 170 Index 175 Index of Symbols 176 Download Not all books on / appear on the homepage. In order not to miss many of them follow Download Link (Ebooks section) (see top of each page on AH) and visit too :)
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