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On the solution of block Hessenberg systems
Author(s) -
Stewart G. W.
Publication year - 1995
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.1680020309
Subject(s) - toeplitz matrix , block (permutation group theory) , mathematics , gaussian elimination , divide and conquer algorithms , algorithm , matrix (chemical analysis) , fast fourier transform , sparse matrix , gaussian , algebra over a field , combinatorics , pure mathematics , physics , materials science , quantum mechanics , composite material
This paper describes a divide‐and‐conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.