Bunch–Kaufman Factorization for Real Symmetric Indefinite Banded Matrices | Zendy

Mark T. Jones | Zendy; Merrell L. Patrick | Zendy

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Bunch–Kaufman Factorization for Real Symmetric Indefinite Banded Matrices

Author(s) -

Mark T. Jones,

Merrell L. Patrick

Publication year - 1993

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/0614039

Subject(s) - factoring , factorization , mathematics , eigenvalues and eigenvectors , lanczos algorithm , incomplete lu factorization , algebra over a field , symmetric matrix , lanczos resampling , matrix (chemical analysis) , algorithm , matrix decomposition , pure mathematics , physics , economics , materials science , finance , quantum mechanics , composite material

The Bunch–Kaufman algorithm for factoring symmetric indefinite matrices has been rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using the Lanczos method, the Bunch–Kaufman algorithm does not result in major destruction of the bandwidth. Space/time complexities of the algorithm are given and used to show that the Bunch–Kaufman algorithm is a significant improvement over banded LU factorization. Timing comparisons are used to show the advantage held by the authors’ implementation of Bunch–Kaufman over the implementation of the multifrontal algorithm for indefinite factorization in MA27 when factoring this subclass of matrices.

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