We present an algorithm for solving a linear system in a symmetric M-matrix. In particular, for n × n symmetric M-matrix M , we show how to find a diagonal matrix D such that DMD is diagonallydominant. To compute D, the algorithm must solve O (log n) linear systems in diagonally-dominant matrices. If we solve these diagonallydominant systems approximately using the Spielman-Teng nearly-linear t...

Variable screening is a fast dimension reduction technique for assisting high dimensional feature selection. As a preselection method, it selects a moderate size subset of candidate variables for further refining via feature selection to produce the final model. The performance of variable screening depends on both computational efficiency and the ability to dramatically reduce the number of va...

and Applied Analysis 3 where T is a given positive constant, aij : R → R, i, j 1, . . . , d, are continuous functions and τij > 0 for i, j 1, . . . , d with i / j. Define r : max { τij : i, j 1, . . . , d, i / j } . 2.2 Note that 2.1 is a special case of 1.2 . More precisely, the right hand side of 2.1 equals f t, xt , where f f1, . . . , fd : 0, T × C → R is defined as follows: fi ( t, φ ) : a...

In this note, we bound the inverse of nonsingular diagonal dominant matrices under the infinity norm. This bound is always sharper than the one in [P.N. Shivakumar, et al., On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital dynamics, SIAM J. Matrix Anal. Appl. 17 (2) (1996) 298–312]. c © 2008 Published by Elsevier Ltd

In this paper, new error bounds for the linear complementarity problem are obtained when the involved matrix is a weakly chained diagonally dominant B-matrix. The proposed error bounds are better than some existing results. The advantages of the results obtained are illustrated by numerical examples.

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...

It is well known that standard incomplete factorization (IC) methods exist for M-matrices 14] and that modiied incomplete factorization (MIC) methods exist for weakly diagonally dominant matrices 8]. The restriction to these classes of matrices excludes many realistic general applications to discretized partial diieren-tial equations. We present a technique to avoid this problem by making an in...

We present a structured perturbation theory for the LDU factorization of (row) diagonally dominant matrices and we use this theory to prove that a recent algorithm of Ye (Math Comp 77(264):2195–2230, 2008) computes the L , D andU factors of these matrices with relative errors less than 14n3u, where u is the unit roundoff and n × n is the size of the matrix. The relative errors for D are compone...