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This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, ...

The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision ...

We present a structured parallel geometry-based multifrontal sparse solver using hierarchically semiseparable (HSS) representations and exploiting the inherent low-rank structures. Parallel strategies for nested dissection ordering (taking low rankness ...

On many current and emerging computing architectures, single-precision calculations are at least twice as fast as double-precision calculations. In addition, the use of single precision may reduce pressure on memory bandwidth. The penalty for using ...

In this paper, we present a new way to improve performance of the factorization of large sparse linear systems which cannot fit in memory. Instead of rewriting a large part of the code to implement an out-of-core algorithm with explicit I/O, we modify ...

An ANSI C code for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre-ordering and symbolic analysis phase computes an upper bound on ...

A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fill-...

We introduce a new code for the direct solution of sparse symmetric linear equations that solves indefinite systems with 2 × 2 pivoting for stability. This code, called MA57, is in HSL 2002 and supersedes the well used HSL code MA27. We describe some of ...

In the recently presented sparse matrix extension of MATLAB, there is no routine for sparse QR factorization. Sparse linear least-squares problems are instead solved by the augmented system method. The accuracy in computed solutions is strongly dependent ...