Abstract
The rank-one modification algorithm of theLDM t factorization was given by Bennett [1]. His method, however, could break down even when the matrix is nonsingular and well-conditioned. We introduce a pivoting strategy for avoiding possible break-down as well as for suppressing error growth in the modification process. The method is based on a symbolic formula of the rank-one modification of the factorization of a possibly singular nonsymmetric matrix. A new symbolic formula is also obtained for the inverses of the factor matrices. Repeated application of our method produces theLDM t-like product form factorization of a matrix. A numerical example is given to illustrate our pivoting method. An incomplete factorization algorithm is also introduced for updating positive definite matrix useful in quasi-Newton methods, in which the Fletcher and Powell algorithm [2] and the Gill, Murray and Saunders algorithm [4] are usually used.
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This paper is presented at the Japan SIAM Annual Meeting held at University of Tokyo, Japan, October 7–9, 1991.
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Tanabe, K., Sagae, M. Pivoting strategy for rank-one modification ofLDM t-like factorization. Numer Algor 2, 137–153 (1992). https://doi.org/10.1007/BF02145382
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DOI: https://doi.org/10.1007/BF02145382