Operator Theory: Advances and Applications

Separable Type Representations of Matrices and Fast Algorithms

Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms

Authors: Eidelman, Yuli, Gohberg, Israel, Haimovici, Iulian

  • Self-contained monograph with material developed over the last 30 years
  • Systematic theoretical and computational study of several types of generalizations of separable matrices
  • Many illustrative examples in different chapters of the book
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About this book

This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work is focused on algorithms of multiplication, inversion and description of eigenstructure and includes a large number of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part contains factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structure. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and the accessible style the text will be useful to engineers, scientists, numerical analysts, computer scientists and mathematicians alike.​

Table of contents (20 chapters)

  • Matrices with Separable Representation and Low Complexity Algorithms

    Eidelman, Yuli (et al.)

    Pages 3-44

  • The Minimal Rank Completion Problem

    Eidelman, Yuli (et al.)

    Pages 45-66

  • Matrices in Diagonal Plus Semiseparable Form

    Eidelman, Yuli (et al.)

    Pages 67-73

  • Quasiseparable Representations: The Basics

    Eidelman, Yuli (et al.)

    Pages 75-84

  • Quasiseparable Generators

    Eidelman, Yuli (et al.)

    Pages 85-117

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0606-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-3-0348-0605-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Separable Type Representations of Matrices and Fast Algorithms
Book Subtitle
Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
234
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0606-0
DOI
10.1007/978-3-0348-0606-0
Hardcover ISBN
978-3-0348-0605-3
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XV, 399
Topics