The Gauss-Huard algorithm and LU factorization

The Gauss-Huard algorithm and LU factorization

In this paper we analyze the Gauss-Huard algorithm. From a description of the algorithm in terms of matrix-vector operations we reveal a close relation between the Gauss-Huard algorithm and an LU factorization as constructed in an ikj variant.

LU-AD1 Factorization Algorithm

CALU: A Communication Optimal LU Factorization Algorithm

Since the cost of communication (moving data) greatly exceeds the cost of doing arithmetic on current and future computing platforms, we are motivated to devise algorithms that communicate as little as possible, even if they do slightly more arithmetic, and as long as they still get the right answer. This paper is about getting the right answer for such an algorithm. It discusses CALU, a commun...

Stability of Gauss-Huard Elimination for Solving Linear Systems

This paper considers elimination methods to solve dense linear systems, in particular a variant due to Huard of Gaussian elimination [13]. This variant reduces the system to an equivalent diagonal system just as GaussJordan elimination, but does not require more floating-point operations than Gaussian elimination. Huard's method may be advantageous for use in computers with hierarchical memory,...

Variable-Size Batched Gauss-Huard for Block-Jacobi Preconditioning

In this work we present new kernels for the generation and application of block-Jacobi preconditioners that accelerate the iterative solution of sparse linear systems on graphics processing units (GPUs). Our approach departs from the conventional LU factorization and decomposes the diagonal blocks of the matrix using the Gauss-Huard method. When enhanced with column pivoting, this method is as ...