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Structured Matrices and Polynomials

Bag om Structured Matrices and Polynomials

Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.

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  • Sprog:
  • Engelsk
  • ISBN:
  • 9781461266259
  • Indbinding:
  • Paperback
  • Sideantal:
  • 308
  • Udgivet:
  • 23. oktober 2012
  • Størrelse:
  • 155x17x235 mm.
  • Vægt:
  • 470 g.
  • 8-11 hverdage.
  • 16. januar 2025
På lager
Forlænget returret til d. 31. januar 2025
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Beskrivelse af Structured Matrices and Polynomials

Structured matrices serve as a natural bridge between the areas of
algebraic computations with polynomials and numerical matrix
computations, allowing cross-fertilization of both fields. This book
covers most fundamental numerical and algebraic computations with
Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured
matrices. Throughout the computations, the matrices are represented by
their compressed images, called displacements, enabling both a unified
treatment of various matrix structures and dramatic saving of computer
time and memory. The resulting superfast algorithms allow further
dramatic parallel acceleration using FFT and fast sine and cosine
transforms.
Included are specific applications to other fields, in
particular, superfast solutions to: various fundamental problems of
computer algebra; the tangential Nevanlinna--Pick and matrix Nehari
problems
The primary intended readership for this work includes
researchers, algorithm designers, and advanced graduate students in
the fields of computations with structured matrices, computer algebra,
and numerical rational interpolation. The book goes beyond research
frontiers and, apart from very recent research articles, includes yet
unpublished results.
To serve a wider audience, the presentation unfolds
systematically and is written in a user-friendly engaging style. Only
some preliminary knowledge of the fundamentals of linear algebra is
required. This makes the material accessible to graduate students and
new researchers who wish to study the rapidly exploding area of
computations with structured matrices and polynomials. Examples,
tables, figures, exercises, extensive bibliography, and index lend
this text to classroom use or self-study.

Brugerbedømmelser af Structured Matrices and Polynomials