Fast Stable Solvers for Sequentially Semi-Seperable Linear Systems of Equations

Chandrasekaran, S ; DeWilde, P ; Gu, M ; Pals, T ; van der Veen, A J ; White, D A

Lawrence Livermore National Laboratory

关键词: Matrices;    Integral Equations;    Algorithms;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;   

DOI  :  10.2172/15003389
RP-ID  :  UCRL-CR-151499
RP-ID  :  W-7405-ENG-48
RP-ID  :  15003389

美国|英语

来源: UNT Digital Library

【 摘 要 】

We define the class of sequentially semi-separable matrices in this paper. Essentially this is the class of matrices which have low numerical rank on their off diagonal blocks. Examples include banded matrices, semi-separable matrices, their sums as well as inverses of these sums. Fast and stable algorithms for solving linear systems of equations involving such matrices and computing Moore-Penrose inverses are presented. Supporting numerical results are also presented. In addition, fast algorithms to construct and update this matrix structure for any given matrix are presented. Finally, numerical results that show that the coefficient matrices resulting from global spectral discretizations of certain integral equations indeed have this matrix structure are given.