An out-of-core sparse symmetric-indefinite factorization method

Issues in the Design of Scalable Out-of-Core Dense Symmetric Indefinite Factorization Algorithms

New Pivot Selection for Sparse Symmetric Indefinite Factorization

We propose a new pivot selection technique for symmetric indefinite factorization of sparse matrices. Such factorization should maintain both sparsity and numerical stability of the factors, both of which depend solely on the choices of the pivots. Our method is based on the minimum degree algorithm and also considers the stability of the factors at the same time. Our experiments show that our ...

Communication-Avoiding Symmetric-Indefinite Factorization

We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen’s triangular tridiagonalization. It factors a dense symmetric matrix A as the product A = PLTLP where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding fac...

Efficient Methods for Out-of-Core Sparse Cholesky Factorization

We consider the problem of sparse Cholesky factorization with limited main memory. The goal is to e ciently factor matrices whose Cholesky factors essentially ll the available disk storage, using very little memory (as little as 16 Mbytes). This would enable very large industrial problems to be solved with workstations of very modest cost. We consider three candidate algorithms. Each is based o...

High-Performance Out-of-Core Sparse LU Factorization

We present an out-of-core sparse nonsymmetric LU -factorization algorithm with partial pivoting. We have implemented the algorithm and our experiments show that it can easily factor matrices whose factors are larger than main memory at rates comparable to those of an in-core solver. The algorithm is novel in several respects, including the use of panels that are larger than memory and the use o...