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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 to… (More)

- Xiaoye S. Li, James Demmel
- ACM Trans. Math. Softw.
- 2003

We present the main algorithmic features in the software package SuperLU_DIST, a distributed-memory sparse direct solver for large sets of linear equations. We give in detail our parallelization strategies, with a focus on scalability issues, and demonstrate the software's parallel performance and scalability on current machines. The solver is based on… (More)

- James Demmel, John R. Gilbert, Xiaoye S. Li
- SIAM J. Matrix Analysis Applications
- 1999

Although Gaussian elimination with partial pivoting is a robust algorithm to solve unsymmetric sparse linear systems of equations, it is difficult to implement efficiently on parallel machines because of its dynamic and somewhat unpredictable way of generating work and intermediate results at run time. In this paper, we present an efficient parallel… (More)

- Yozo Hida, Xiaoye S. Li, David H. Bailey
- IEEE Symposium on Computer Arithmetic
- 2001

A quad-double number is an unevaluated sum of four IEEE double precision numbers, capable of representing at least 212 bits of significand. We present the algorithms for various arithmetic operations (including the four basic operations and various algebraic and transcendental operations) on quad-double numbers. The performance of the algorithms,… (More)

Sparse Gaussian Elimination on High Performance Computers

- Jianlin Xia, Shivkumar Chandrasekaran, Ming Gu, Xiaoye S. Li
- SIAM J. Matrix Analysis Applications
- 2009

In this paper we develop a fast direct solver for large discretized linear systems using the supernodal multifrontal method together with low-rank approximations. For linear systems arising from certain partial differential equations such as elliptic equations, during the Gaussian elimination of the matrices with proper ordering, the fill-in has a low-rank… (More)

- Xiaoye S. Li, James Demmel, +10 authors Daniel J. Yoo
- ACM Trans. Math. Softw.
- 2002

This article describes the design rationale, a C implementation, and conformance testing of a subset of the new Standard for the BLAS (Basic Linear Algebra Subroutines): Extended and Mixed Precision BLAS. Permitting higher internal precision and mixed input/output types and precisions allows us to implement some algorithms that are simpler, more accurate,… (More)

- Jianlin Xia, Shivkumar Chandrasekaran, Ming Gu, Xiaoye S. Li
- Numerical Lin. Alg. with Applic.
- 2010

Semiseparable matrices and many other rank-structured matrices have been widely used in developing new fast matrix algorithms. In this paper, we generalize the hierarchically semiseparable (HSS) matrix representations and propose some fast algorithms for HSS matrices. We represent HSS matrices in terms of general binary HSS trees and use simplified… (More)

- Xiaoye S. Li, James Demmel
- SC
- 1998

We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting is that it permits <i>a priori</i> determination of data structures… (More)

This paper describes a new software package for performing arithmetic with an arbitrarily high level of numeric precision. It is based on the earlier MPFUN package [2], enhanced with special IEEE floating-point numerical techniques and several new functions. This package is written in C++ code for high performance and broad portability and includes both C++… (More)