Fast inversion algorithms for diagonal plus semiseparable matrices

Y. Eidelman, I. Gohberg

Research output: Contribution to journalArticlepeer-review

Abstract

Here are considered matrices represented as a sum of diagonal and semiseparable ones. These matrices belong to the class of structured matrices which arises in numerous applications. Fast O(N) algorithms for their inversion were developed before under additional restrictions which are a source of instability. Our aim is to eliminate these restrictions and to develop reliable and stable numerical algorithms. In this paper we obtain such algorithms with the only requirement that the considered matrix is invertible and its determinant is not close to zero. The case of semiseparable matrices of order one was considered in detail in an earlier paper of the authors.

Original languageEnglish
Pages (from-to)165-183
Number of pages19
JournalIntegral Equations and Operator Theory
Volume27
Issue number2
DOIs
StatePublished - 1997

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