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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 to perform most of the numerical computation in dense matrix kernels. We introduce unsymmetric supernode-panel updates and two-dimensional data partitioning toâ€¦ (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 satisfy a condition F (x) + F'(xk) sk _< F(x)II for a "forcing term" r/ [0, 1). In typical applications, the choice of the forcing terms is critical to theâ€¦ (More)

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

- 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 linear model of F. Here, inexact Newton methods are formulated that incorporate features designed to improve convergence from arbitrary starting points. Forâ€¦ (More)

- James Demmel, Ming Gu, Stanley C. Eisenstat, Ivan Slapni
- 1997

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 correct digits, even if the singular values have widely varying magnitudes. This is in contrast to the absolute accuracy provided by conventional backward stableâ€¦ (More)

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

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

- Stanley C. Eisenstat, Joseph W. H. Liu
- SIAM J. Scientific Computing
- 1993

- Cleve Ashcraft, Stanley C. Eisenstat, Joseph W. H. Liu
- SIAM J. Scientific Computing
- 1990

This paper presents a column-oriented distributed algorithm for factoring a large sparse symmetric positive definite matrix on a local-memory parallel processor. Processors cooperate in computing each column of the Cholesky factor by calculating independent updates to the corresponding column of the original matrix. These updates are sent in a fan-in mannerâ€¦ (More)

- Stanley C. Eisenstat, Ilse C. F. Ipsen
- SIAM J. Matrix Analysis Applications
- 1998

We show that three well-known perturbation bounds for matrix eigenvalues imply relative bounds: the Bauer-Fike and Hooman-Wielandt theorems for diagonalisable matrices, and Weyl's theorem for Hermitian matrices. As a consequence, relative perturbation bounds are not necessarily stronger than absolute bounds; and the conditioning of an eigenvalue in theâ€¦ (More)