Operator Theory: Advances and Applications

Separable Type Representations of Matrices and Fast Algorithms

Volume 2 Eigenvalue Method

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 second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods to compute eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms being derived also for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable of any order representations is studied in the third part. This method is then used in the last part in order to get a fast solver for the polynomial root finding problem. 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 (16 chapters)

  • Quasiseparable of Order One Matrices.Characteristic Polynomials

    Eidelman, Yuli (et al.)

    Pages 3-12

  • Eigenvalues with Geometric Multiplicity One

    Eidelman, Yuli (et al.)

    Pages 13-31

  • Kernels of Quasiseparable of Order One Matrices

    Eidelman, Yuli (et al.)

    Pages 33-49

  • Multiple Eigenvalues

    Eidelman, Yuli (et al.)

    Pages 51-71

  • Divide Step

    Eidelman, Yuli (et al.)

    Pages 75-93

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-0612-1
  • 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 978-3-0348-0611-4
  • 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 2 Eigenvalue Method
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
235
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0612-1
DOI
10.1007/978-3-0348-0612-1
Hardcover ISBN
978-3-0348-0611-4
Series ISSN
0255-0156
Edition Number
1
Number of Pages
XI, 359
Topics