TY - JOUR

T1 - Out-of-band quasiseparable matrices

AU - Eidelman, Y.

AU - Gohberg, I.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - We study structured matrices which consist of a band part and quasiseparable parts below and upper the band. We extend algorithms known for quasiseparable matrices, i.e. for the case when the band consists of the main diagonal only, to a wider class of matrices. The matrices which we consider may be treated as an usual quasiseparable matrices with larger orders of generators. Hence one can apply the methods developed for usual quasiseparable matrices and obtain various linear complexity O (N) algorithms. However in this case the coefficients in N in the complexity estimates turns out to be quite large. In this paper we use the structure more accurately by division of the matrix into three parts in which the middle part is the band instead of diagonal as it is used for usual quasiseparable matrices. This approach allows to use better the structure of the matrix in order to improve the coefficients in N in the complexity estimates for the algorithms. This method works for algorithms which keep invariant the structure.

AB - We study structured matrices which consist of a band part and quasiseparable parts below and upper the band. We extend algorithms known for quasiseparable matrices, i.e. for the case when the band consists of the main diagonal only, to a wider class of matrices. The matrices which we consider may be treated as an usual quasiseparable matrices with larger orders of generators. Hence one can apply the methods developed for usual quasiseparable matrices and obtain various linear complexity O (N) algorithms. However in this case the coefficients in N in the complexity estimates turns out to be quite large. In this paper we use the structure more accurately by division of the matrix into three parts in which the middle part is the band instead of diagonal as it is used for usual quasiseparable matrices. This approach allows to use better the structure of the matrix in order to improve the coefficients in N in the complexity estimates for the algorithms. This method works for algorithms which keep invariant the structure.

KW - Linear complexity algorithms

KW - Quasiseparable matrices

KW - Structured matrices

UR - http://www.scopus.com/inward/record.url?scp=42749097568&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2008.02.026

DO - 10.1016/j.laa.2008.02.026

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AN - SCOPUS:42749097568

SN - 0024-3795

VL - 429

SP - 266

EP - 289

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -