The Resource Exact constants in approximation theory, N. Korneichuk ; translated from the Russian by K. Ivanov, (electronic resource)

Exact constants in approximation theory, N. Korneichuk ; translated from the Russian by K. Ivanov, (electronic resource)

Label
Exact constants in approximation theory
Title
Exact constants in approximation theory
Statement of responsibility
N. Korneichuk ; translated from the Russian by K. Ivanov
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
A self-contained introduction for non-specialists, or a reference work for experts, on the area of approximation theory concerned with exact constants
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Korneĭchuk, Nikolaĭ Pavlovich
Dewey number
  • 511.4
  • 511/.4
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA221
LC item number
.K6613 1990
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Ivanov, K
Series statement
  • Encyclopedia of mathematics and its applications
  • Encyclopedia of Mathematics and its Applications
Series volume
  • v. 38
  • v.38
http://library.link/vocab/subjectName
Approximation theory
Label
Exact constants in approximation theory, N. Korneichuk ; translated from the Russian by K. Ivanov, (electronic resource)
Instantiates
Publication
Note
Translation of: Tochnye konstanty v teorii priblizhenii͡a
Bibliography note
Includes bibliographical references (p. 426-449) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Series Page; Title; Copyright; CONTENTS; PREFACE; LIST OF MOST IMPORTANT NOTATION; 1 Best approximation and duality in extremal problems; 1.1 Best approximation; 1.2 Formulation of extremal problems; 1.3 Duality of extremal problems in linear spaces; 1.4 Duality in functional spaces; 1.5 Duality for best approximation of classes of functions; Comments; Exercises; 2 Polynomials and spline functions as approximating tools; 2.1 Polynomials of best approximation; 2.2 Linear methods for polynomial approximation, Lebesgue constants; 2.3 Polynomial splines
  • 2.4 Spline interpolation2.5 On the existence of perfect splines with prescribed zeros; Comments; Exercises; 3 Comparison theorems and inequalities for the norms of functions and their derivatives; 3.1 Standard splines; 3.2 Comparison theorems in general cases; 3.3 Comparison theorems and exact inequalities for differentiable functions; 3.4 Internal extremal properties of splines; 3.5 Inequalities for polynomials; Comments; Other results and exercises; 4 Polynomial approximation of classes of functions with bounded rth derivative in Lp; 4.1 Minimizing the error in the class of A-methods
  • 4.2 The supremums of the best approximations of classes Wrp by trigonometric polynomials4.3 Approximation by partial sums of Fourier series, their means and analogs; 4.4 Approximation by algebraic polynomials on an interval; Comments; Other results and exercises; 5 Spline approximation of classes of functions with a bounded rth derivative; 5.1 Inequalities for functions with prescribed zeros; 5.2 The interpolation error of the periodic splines with minimal defect on classes Wrp; 5.3 Estimates for spline interpolation on classes Wrp[a,b]; 5.4 Best approximation by splines of minimal defect
  • CommentsOther results and exercises; 6 Exact constants in Jackson inequalities; 6.1 Modulus of continuity and general statement of the problems; 6.2 Jackson inequalities for polynomial approximations; 6.3 Jackson-type inequalities for spline approximation; Comments; Other results and exercises; 7 Approximation of classes of functions determined by modulus of continuity; 7.1 General facts and Σ-rearrangements; 7.2 Exact results for the best approximation of classes WrHw, WrHw[a,b]; 7.3 Approximation by linear methods; Comments; Other results and exercises
  • 8 N-widths of functional classes and closely related extremal problems8.1 N-widths of classes of functions with bounded rth derivatives; 8.2 N-widths of classes defined by the modulus of continuity; 8.3 Closely related extremal problems; Comments; Other results and exercises; APPENDIX; A1 Hölder and Minkowski inequalities and some extremal relations; A2 Steklov functions; A3 Proofs of comparison theorems for Σ-rearrangements; 1 Auxiliary results; 2 Proofs of Theorems 7.1.4 and 7.1.5; 3 Proof of theorem 7.1.6; REFERENCES; I Monographs; A Monographs on approximation theory; B Other books
  • II Articles
Dimensions
unknown
Extent
1 online resource (466 p.)
Form of item
online
Isbn
9781107088115
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000343945
  • (EBL)1179085
  • (SSID)ssj0000857567
  • (PQKBManifestationID)11539487
  • (PQKBTitleCode)TC0000857567
  • (PQKBWorkID)10856325
  • (PQKB)11699805
  • (UkCbUP)CR9781107325791
  • (MiAaPQ)EBC1179085
  • (EXLCZ)992670000000343945
Label
Exact constants in approximation theory, N. Korneichuk ; translated from the Russian by K. Ivanov, (electronic resource)
Publication
Note
Translation of: Tochnye konstanty v teorii priblizhenii͡a
Bibliography note
Includes bibliographical references (p. 426-449) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Series Page; Title; Copyright; CONTENTS; PREFACE; LIST OF MOST IMPORTANT NOTATION; 1 Best approximation and duality in extremal problems; 1.1 Best approximation; 1.2 Formulation of extremal problems; 1.3 Duality of extremal problems in linear spaces; 1.4 Duality in functional spaces; 1.5 Duality for best approximation of classes of functions; Comments; Exercises; 2 Polynomials and spline functions as approximating tools; 2.1 Polynomials of best approximation; 2.2 Linear methods for polynomial approximation, Lebesgue constants; 2.3 Polynomial splines
  • 2.4 Spline interpolation2.5 On the existence of perfect splines with prescribed zeros; Comments; Exercises; 3 Comparison theorems and inequalities for the norms of functions and their derivatives; 3.1 Standard splines; 3.2 Comparison theorems in general cases; 3.3 Comparison theorems and exact inequalities for differentiable functions; 3.4 Internal extremal properties of splines; 3.5 Inequalities for polynomials; Comments; Other results and exercises; 4 Polynomial approximation of classes of functions with bounded rth derivative in Lp; 4.1 Minimizing the error in the class of A-methods
  • 4.2 The supremums of the best approximations of classes Wrp by trigonometric polynomials4.3 Approximation by partial sums of Fourier series, their means and analogs; 4.4 Approximation by algebraic polynomials on an interval; Comments; Other results and exercises; 5 Spline approximation of classes of functions with a bounded rth derivative; 5.1 Inequalities for functions with prescribed zeros; 5.2 The interpolation error of the periodic splines with minimal defect on classes Wrp; 5.3 Estimates for spline interpolation on classes Wrp[a,b]; 5.4 Best approximation by splines of minimal defect
  • CommentsOther results and exercises; 6 Exact constants in Jackson inequalities; 6.1 Modulus of continuity and general statement of the problems; 6.2 Jackson inequalities for polynomial approximations; 6.3 Jackson-type inequalities for spline approximation; Comments; Other results and exercises; 7 Approximation of classes of functions determined by modulus of continuity; 7.1 General facts and Σ-rearrangements; 7.2 Exact results for the best approximation of classes WrHw, WrHw[a,b]; 7.3 Approximation by linear methods; Comments; Other results and exercises
  • 8 N-widths of functional classes and closely related extremal problems8.1 N-widths of classes of functions with bounded rth derivatives; 8.2 N-widths of classes defined by the modulus of continuity; 8.3 Closely related extremal problems; Comments; Other results and exercises; APPENDIX; A1 Hölder and Minkowski inequalities and some extremal relations; A2 Steklov functions; A3 Proofs of comparison theorems for Σ-rearrangements; 1 Auxiliary results; 2 Proofs of Theorems 7.1.4 and 7.1.5; 3 Proof of theorem 7.1.6; REFERENCES; I Monographs; A Monographs on approximation theory; B Other books
  • II Articles
Dimensions
unknown
Extent
1 online resource (466 p.)
Form of item
online
Isbn
9781107088115
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000343945
  • (EBL)1179085
  • (SSID)ssj0000857567
  • (PQKBManifestationID)11539487
  • (PQKBTitleCode)TC0000857567
  • (PQKBWorkID)10856325
  • (PQKB)11699805
  • (UkCbUP)CR9781107325791
  • (MiAaPQ)EBC1179085
  • (EXLCZ)992670000000343945

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