SUMMARY We describe a novel technique for computing a sparse incomplete factorization of a general symmetric positive deenite matrix A. The factorization is not based on the Cholesky algorithm (or Gaussian elimination), but on A{orthogonalization. Thus, the incomplete factorization always exists and can be computed without any diagonal modiication. When used in conjunction with the conjugate gr...

Extended Abstract In this paper, we present a class of graph-based preconditioners for sparse linear systems arising from the finite element discretization of elliptic partial differential equations. A sparse matrix can be preconditioned by using a subgraph of its weighted adjacency matrix. The subgraph can be viewed as a " support graph " and the corresponding sparse matrix can be used as a pr...

H-Matrix LU-decomposition based preconditioners for BEM

Sparse approximate inverse preconditioners have attracted much attention recently, because of their potential usefulness in a parallel environment. In this paper, we explore several performance issues related to effective sparse approximate inverse preconditioners (SAIPs) for the matrices derived from PDEs. Our refinements can significantly improve the quality of existing SAIPs and/or reduce th...

We present a new preconditioner for linear systems arising from finite-elements discretizations of scalar elliptic partial differential equations (pde’s). The solver splits the collection {Ke} of element matrices into a subset E(t) of matrices that are approximable by diagonally-dominant matrices and a subset of matrices that are not approximable. The approximable Ke’s are approximated by diago...

We present a new preconditioner for linear systems arising from finite-element discretizations of scalar elliptic partial differential equations (PDE’s). The solver splits the collection {Ke} of element matrices into a subset of matrices that are approximable by diagonally dominant matrices and a subset of matrices that are not approximable. The approximable Ke’s are approximated by diagonally ...

We develop a drop-threshold incomplete Cholesky preconditioner which uses blocked data structures and computational kernels for improved performance on computers with one or more levels of cache memory. The techniques are similar to those used for Cholesky factorization in sparse direct solvers. We report on the performance of our preconditioned conjugate gradient solver on sparse linear system...

In this paper, we discuss eecient implementation of a new class of preconditioners for linear systems arising from interior point methods. These new preconditioners give superior performancenear the solution of a linear programming problem where the linear systems are typically highly ill-conditioned. They rely upon the computation of an LU factorization of a subset of columns of the matrix of ...

This paper presents a general preconditioning method based on a multilevel partial solution approach. The basic step in constructing the preconditioner is to separate the initial points into two subsets. The rst subset which can be termed \coarse" is obtained by using \block" independent sets, or \aggregates". Two aggregates have no coupling between them, but nodes in the same aggregate may be ...

Sparse linear systems are ubiquitous in various scientific computing applications. Inversion of sparse matrices with standard direct solve schemes are prohibitive for large systems due to their quadratic/cubic complexity. Iterative solvers, on the other hand, demonstrate better scalability. However, they suffer from poor convergence rates when used without a preconditioner. There are many preco...