Operator Theory: Advances and Applications

Separable Type Representations of Matrices and Fast Algorithms

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

  • Self-contained two-volume 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
see more benefits

Buy this book

Hardcover $209.00
price for USA
  • ISBN 978-3-0348-0728-9
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
About this book

This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in 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 includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike. 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 for computing 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 also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide 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 accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.

Buy this book

Hardcover $209.00
price for USA
  • ISBN 978-3-0348-0728-9
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Separable Type Representations of Matrices and Fast Algorithms
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
234/235
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
0b01e83280c78fe2
Hardcover ISBN
978-3-0348-0728-9
Series ISSN
0255-0156
Edition Number
1
Number of Pages
788
Topics