We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix A ∈ Cn×n. We are also able to predict which permutation matrices will be chosen by partial pivoting or complete pivoting Gaussian elimination. Our method uses maxplus algebra and is based purely on the modulii of the entries in the matrix. This approximation can be used ...

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matri...

BACKGROUND Currently, a suitable and reliable noninvasive method to evaluate rotational stability in vivo in anterior cruciate ligament-deficient knees, particularly during sports movements, does not exist. We speculated that if there is a rotational instability, the patient would avoid reaching a high pivoting moment during pivoting activities as a defense mechanism, and that the ground reacti...

Gaussian elimination with partial pivoting is unstable in the worst case: the "growth factor" can be as large as 2"-l, where n is the matrix dimension, resulting in a loss of n bits of precision. It is proposed that an average-case analysis can help explain why it is nevertheless stable in practice. The results presented begin with the observation that for many distributions of matrices, the ma...

This document presents the Schur-decomposition based dynamic pivoting method for GLU solver. The new pivoting method allows dynamic pivoting for small number of small valued pivots after the AMD (approximate minimum degree) ordering process and the symbolic analysis process in the GLU, which is similar to the left-looking method. This method will not be very effective if there is a large number...

The Crout variant of ILU preconditioner (ILUC) developed recently has been shown to have a number of advantages over ILUT, the conventional row-based ILU preconditioner [14]. This paper explores pivoting strategies for sparse symmetric matrices to improve the robustness of ILUC. This paper shows how to integrate two symmetry-preserving pivoting strategies, the diagonal pivoting and the Bunch-Ka...

Consider the linear system of equations of the form Ax = b where the coefficient matrix A ∈ Rn×n is nonsingular, large, sparse and nonsymmetric and also x, b ∈ R. We refer to this system as the original system. An explicit preconditioner M for this system is an approximation of matrix A−1. In [1], Lou presented the Backward Factored INVerse or BFINV algorithm which computes the inverse factoriz...