A look-ahead Schur algorithm
(1994) Fifth SIAM Conference on Applied Linear Algebra — Location: Snowbird, USA
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- Abstract
- The classical Schur algorithm computes the LDL T factorization of a symmetric Toeplitz matrix in O(n 2 ) operations, but requires that all the principal minors of the matrix be nonsingular. Look-ahead schemes have been proposed to deal with matrices that have exactly singular principal minors [9], [11]. Unfortunately, these algorithms cannot be extended to matrices that have ill-conditioned principal minors. Consequently, the relative errors obtained using the classical Schur algorithm on matrices having ill-conditioned principal minors is very poor. In this paper, we propose a look-ahead scheme for such matrices and present empirical results which demonstrate the improvement over the classical Schur algorithm for symmetric Toeplitz matrices with ill-conditioned principal minors.
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Gallivan, K., Thirumalai, S., & Van Dooren, P. (1994). A look-ahead Schur algorithm. Fifth SIAM Conference on Applied Linear Algebra, Snowbird, USA. https://hdl.handle.net/2078.5/228998