TY - JOUR
T1 - A modification of the Dewilde-van der Veen method for inversion of finite structured matrices
AU - Eidelman, Y.
AU - Gohberg, I.
N1 - Publisher Copyright:
© 2002 Elsevier Science Inc. All rights reserved.
PY - 2002/3/1
Y1 - 2002/3/1
N2 - We study a class of block structured matrices R={Rij}i,j=1N with a property that the solution of the corresponding system Rx=y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference. The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments.
AB - We study a class of block structured matrices R={Rij}i,j=1N with a property that the solution of the corresponding system Rx=y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference. The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments.
KW - Factorization algorithms
KW - Inversion algorithms
KW - Linear complexity algorithms
KW - Solution of linear equations
KW - Structured matrices
UR - http://www.scopus.com/inward/record.url?scp=31244431952&partnerID=8YFLogxK
U2 - 10.1016/S0024-3795(01)00363-9
DO - 10.1016/S0024-3795(01)00363-9
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:31244431952
SN - 0024-3795
VL - 343
SP - 419
EP - 450
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -