UID:
almafu_9959240254102883
Umfang:
1 online resource (lv, 237 pages) :
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digital, PDF file(s).
ISBN:
1-139-88615-0
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1-107-10235-9
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1-107-08753-8
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1-107-09982-X
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1-107-09377-5
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0-511-66295-5
Serie:
Encyclopedia of mathematics and its applications v. 19
Inhalt:
This reference book provides the main definitions, theorems and techniques in the theory of Birkhoff interpolation by polynomials. The book begins with an article by G. G. Lorentz that discusses some of the important developments in approximation and interpolation in the last twenty years. It presents all the basic material known at the present time in a unified manner. Topics discussed include; applications of Birkhoff interpolation to approximation theory, quadrature formulas and Chebyshev systems; lacunary interpolation at special knots and an introduction to the theory of Birkhoff interpolation by splines.
Anmerkung:
Imprint from label on t.p. verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley, Advanced Book Program/World Science Division, 1983.
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Publication taken over by Cambridge University Press in 1984 with a new copyright date.
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Includes indexes.
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Cover; Half Title; Series Page; Title; Copyright; Contents; Editor's Statement; Preface; Introduction: Approximation and Interpolation in the Last 20 Years; Chapter 1 Basic Definitions and Properties; 1.1. INTRODUCTION; 1.2. BASIC DEFINITIONS; 1.3. THE ALGEBRAIC CASE; 1.4. PÓLYA AND BIRKHOFF MATRICES; 1.5. REGULARITY THEOREMS; 1.6. THE INTERPOLATING POLYNOMIAL; Chapter 2 Further Elementary Theorems; 2.1. ESTIMATION OF THE DEFECT; THEOREM OF BUDAN-FOURIER; 2.2. COUNT OF PÓLYA AND BIRKHOFF MATRICES; 2.3. SYMMETRY; 2.4. TRIGONOMETRIC INTERPOLATION; 2.5. NOTES
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Chapter 3 Coalescence of Rows3.1. INTRODUCTION; 3.2. LEVEL FUNCTIONS AND COALESCENCE; 3.3. COALESCENCE IN A MATRIX; 3.4. SHIFTS AND DIFFERENTIATION OF DETERMINANTS; 3.5. PERMUTATION NUMBERS AND TAYLOR EXPANSIONS; Chapter 4 Applications of Coalescence; 4.1. CONDITIONALLY REGULAR AND STRONGLY SINGULAR MATRICES; 4.2. THE FUNCTION 8(E); 4.3. THE THEOREM OF FERGUSON; 4.4. SINGULARITY AND PERMUTATION NUMBERS; 4.5. APPLICATIONS; 4.6. THE COALESCENCE CONSTANT; SIGNS OF DETERMINANTS; Chapter 5 Rolle Extensions and Independent Sets of Knots; 5.1. ROLLE EXTENSIONS
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5.2. AN AUXILIARY THEOREM5.3. MARKOV'S INEQUALITY AND APPLICATIONS; 5.4. INDEPENDENT SETS OF KNOTS; 5.5. APPLICATIONS; BIRKHOFF SYSTEMS; 5.6. CONTINUITY OF INTERPOLATION; Chapter 6 Singular Matrices; 6.1. INTRODUCTION; SUPPORTED SINGLETONS; 6.2. PROOF OF THEOREM 6.2; 6.3. ALMOST-SIMPLE MATRICES; 6.4. PROBABILITY OF REGULARITY; 6.5. NOTES; Chapter 7 Zeros of Birkhoff Splines; 7.1. BIRKHOFF'S KERNEL; 7.2. BIRKHOFF'S IDENTITY; 7.3. SPLINES; DIAGRAMS, BOUNDARY; 7.4. COUNT OF ZEROS OF SPLINES; 7.5. COROLLARIES; BIRKHOFF-LORENTZ THEOREM
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7.6. APPLICATIONS TO BIRKHOFF INTERPOLATION7.7. NOTES; Chapter 8 Almost-Hermitian Matrices; Special Three-Row Matrices; 8.1. INTRODUCTION; 8.2. ALMOST-HERMITIAN MATRICES; 8.3. RECIPROCAL ALMOST-HERMITIAN MATRICES; 8.4. NULL CURVES FOR THE MATRICES E(p,q; k1,k2); 8.5. THE EXTERIOR SYMMETRIC CASE; 8.6. THE INTERIOR CASE; 8.7. NOTES; Chapter 9 Applications; 9.1. INTRODUCTION; 9.2. MONOTONE APPROXIMATION; 9.3. APPROXIMATION WITH RESTRICTIONS FOR DERIVATIVES; 9.4. THE UNIQUENESS THEOREM; 9.5. SIMULTANEOUS APPROXIMATION; 9.6. CHEBYSHEV SYSTEMS ON [-1, +1]; 9.7. NOTES
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Chapter 10 Birkhoff Quadrature Formulas10.1. DEFINITIONS; q-REGULAR PAIRS E, X; 10.2. q-REGULAR MATRICES; 10.3. PΟĹYA CONDITIONS; GAUSSIAN FORMULAS; 10.4. KERNELS OF QUADRATURE FORMULAS; 10.5. DYN'S THEOREMS; 10.6. NOTES; Chapter 11 Interpolation at the Roots of Unity; 11.1. LACUNARY INTERPOLATION; 11.2. REGULARITY OF (mo,m1,..., mq) INTERPOLATION; 11.3. ESTIMATES ON THE FUNDAMENTAL POLYNOMIALS; 11.4. CONVERGENCE OF INTERPOLATION AT THE ROOTS OF UNITY; 11.5. TRIGONOMETRIC INTERPOLATION; 11.6. NOTES; Chapter 12 Turan's Problem of (0, 2) Interpolation
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12.1. REGULARITY OF SETS OF KNOTS
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English
Weitere Ausg.:
ISBN 0-521-10404-1
Weitere Ausg.:
ISBN 0-521-30239-0
Sprache:
Englisch
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