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- James Demmel, Stanley C. Eisenstat, John R. Gilbert, Xiaoye S. Li, Joseph W. H. Liu
- SIAM J. Matrix Analysis Applications
- 1999

We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. We introduce the notion of unsymmetric supernodes… (More)

- Stanley C. Eisenstat, Howard C. Elman, +5 authors I Ha ; A

Overton, who showed us how the ideal Arnoldi and GMRES problems relate to more general problems of minimization of singular values of functions of matrices 17]. gmres and arnoldi as matrix… (More)

- Stanley C. Eisenstat, Homer F. Walker
- SIAM J. Scientific Computing
- 1996

An inexact Newton method is a generalization ofNewton's method for solving F(x) 0, F n _ _ in, in which, at the kth iteration, the step sk from the current approximate solution xk is required to… (More)

We consider a class of iterative algorithms for solving systems of linear equations where the coefficient matrix is nonsymmetric with positive-definite symmetric part. The algorithms are modelled… (More)

- Ming Gu, Stanley C. Eisenstat
- SIAM J. Scientific Computing
- 1996

Given an m n matrix M with m > n, it is shown that there exists a permutation FI and an integer k such that the QR factorization MYI= Q(Ak ckBk) reveals the numerical rank of M: the k k… (More)

- Stanley C. Eisenstat, Homer F. Walker
- SIAM Journal on Optimization
- 1994

Inexact Newton methods for finding a zero of F 1 1 are variations of Newton's method in which each step only approximately satisfies the linear Newton equation but still reduces the norm of the local… (More)

We analyze when it is possible to compute the singular values and singular vectors of a matrix with high relative accuracy. This means that each computed singular value is guaranteed to have some… (More)

- Ming Gu, Stanley C. Eisenstat
- SIAM J. Matrix Analysis Applications
- 1995

- Ming Gu, Stanley C. Eisenstat
- SIAM J. Matrix Analysis Applications
- 1995

Abstract. The authors present a stable and efficient divide-and-conquer algorithm for computing the singular value decomposition (SVD) of a lower bidiagonal matrix. Previous divide-andconquer… (More)