Abstract
We study divide and conquer method to compute eigenstructure of matrices with quasiseparable representation. In order to find the eigenstructure of a large matrix A we divide the problem into two problems for smaller sized matrices B and C by using the quasiseparable representation of A. In the conquer step we show that to reconstruct the eigenstructure of A from those of B and C amounts to the study of the eigenstructure of a rational matrix function. For a Hermitian matrix A which is order one quasiseparable we completely solve the eigenproblem.
Original language | English |
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Title of host publication | A Panorama of Modern Operator Theory and Related Topics |
Subtitle of host publication | The Israel Gohberg Memorial Volume |
Publisher | Springer Basel |
Pages | 299-328 |
Number of pages | 30 |
ISBN (Electronic) | 9783034802215 |
ISBN (Print) | 9783034802208 |
DOIs | |
State | Published - 1 Jan 2012 |
Keywords
- Divide and conquer
- Hermitian matrix
- Quasiseparable
- Rational matrix function