Overview
- 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
Part of the book series: Operator Theory: Advances and Applications (OT, volume 235)
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Table of contents (16 chapters)
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Front Matter
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The Eigenvalue Structure of Order One Quasiseparable Matrices
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Front Matter
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Divide and Conquer Method for the Eigenproblem
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Front Matter
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Algorithms for QR Iterations and for Reduction to Hessenberg Form
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Front Matter
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QR Iterations for Companion Matrices
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Front Matter
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Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Separable Type Representations of Matrices and Fast Algorithms
Book Subtitle: Volume 2 Eigenvalue Method
Authors: Yuli Eidelman, Israel Gohberg, Iulian Haimovici
Series Title: Operator Theory: Advances and Applications
DOI: https://doi.org/10.1007/978-3-0348-0612-1
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2014
Hardcover ISBN: 978-3-0348-0611-4Published: 18 October 2013
eBook ISBN: 978-3-0348-0612-1Published: 08 October 2013
Series ISSN: 0255-0156
Series E-ISSN: 2296-4878
Edition Number: 1
Number of Pages: XI, 359
Topics: Linear and Multilinear Algebras, Matrix Theory, Numerical Analysis