The Resource Mathematics of approximation, Johan de Villiers, (electronic resource)

Mathematics of approximation, Johan de Villiers, (electronic resource)

Label
Mathematics of approximation
Title
Mathematics of approximation
Statement of responsibility
Johan de Villiers
Creator
Contributor
Provider
Subject
Language
eng
Summary
The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1946-
http://library.link/vocab/creatorName
De Villiers, Johan
Image bit depth
0
LC call number
QA221
LC item number
.D4 2012
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
SpringerLink
Series statement
Mathematics Textbooks for Science and Engineering
Series volume
1
http://library.link/vocab/subjectName
  • Mathematics
  • Mathematical Computing
  • Science
  • Engineering
  • Approximation theory
  • Approximation theory
Label
Mathematics of approximation, Johan de Villiers, (electronic resource)
Instantiates
Publication
Note
Includes index
Antecedent source
mixed
Color
not applicable
Contents
Polynomial Interpolation Formulas -- Error Analysis For Polynomial Interpolation -- Polynomial Uniform Convergence -- Best Approximation -- Approximation Operators -- Best Uniform Polynomial Approximation -- Orthogonality -- Interpolatory Quadrature -- Approximation of Periodic Functions -- Spline Approximation
Dimensions
unknown
Extent
1 online resource.
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9789491216503
Level of compression
uncompressed
Other control number
10.2991/978-94-91216-50-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (OCoLC)798817514
  • (OCoLC)ocn798817514
Label
Mathematics of approximation, Johan de Villiers, (electronic resource)
Publication
Note
Includes index
Antecedent source
mixed
Color
not applicable
Contents
Polynomial Interpolation Formulas -- Error Analysis For Polynomial Interpolation -- Polynomial Uniform Convergence -- Best Approximation -- Approximation Operators -- Best Uniform Polynomial Approximation -- Orthogonality -- Interpolatory Quadrature -- Approximation of Periodic Functions -- Spline Approximation
Dimensions
unknown
Extent
1 online resource.
File format
multiple file formats
Form of item
  • online
  • electronic
Isbn
9789491216503
Level of compression
uncompressed
Other control number
10.2991/978-94-91216-50-3
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (OCoLC)798817514
  • (OCoLC)ocn798817514

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