THE CLASS OF INVERSE M-MATRICES ASSOCIATED TO RANDOM WALKS∗ CLAUDE DELLACHERIE† , SERVET MARTINEZ‡ , AND JAIME SAN MARTIN‡ Abstract. Given W = M−1, with M a tridiagonal M -matrix, we show that there are two diagonal matrices D,E and two nonsingular ultrametric matrices U, V such that DWE is the Hadamard product of U and V . If M is symmetric and row diagonally dominant, we can take D = E = I. W...

In this paper, we use weighted dyadic trees to introduce a new class of nonnegative matrices whose inverses are column diagonally dominant M -matrices.

A suggestive indicator is proposed for predicting whether a given (complex or real) square matrix A is or isn’t a generalized diagonally dominant matrix (GDDM) by which we mean if A can be brought into a strictly diagonally dominant matrix by post-multiplying some diagonal matrix D. Based on the indicator, three self-corrective algorithms are presented for determining if A is or is not a GDDM a...

For a (row) diagonally dominant matrix, if all of its off-diagonal entries and its diagonally dominant parts (which are defined for each row as the absolute value of the diagonal entry subtracted by the sum of the absolute values of off-diagonal entries in that row) are accurately known, we develop an algorithm that computes all the singular values, including zero ones if any, with relative err...

It is well-known that the Schur complement of a strictly diagonally dominant matrix is strictly diagonally dominant, too. Also, if a matrix is an H-matrix, then its Schur complement is an H-matrix, too. Recent research showed that the same type of statement holds for some special subclasses of H-matrices, see, for example, Liu et al. (2004). The aim of this paper is twofold: first, to show that...

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 ...

Convergence analysis of two-grids methods based on coarsening by (unsmoothed) aggregation is presented. For diagonally dominant symmetric (M-)matrices, it is shown that the analysis can be conducted locally; that is, the convergence factor can be bounded above by computing separately for each aggregate a parameter which in some sense measures its quality. The procedure is purely algebraic and c...

We consider a competitive pricing problem where there are multiple firms with limited inventories of substitutable products. Each firm chooses the prices that it charges for its product over a finite selling horizon. The demand of each firm jointly depends on the prices of all firms in a deterministic fashion through a linear demand function. The goal of each firm is to choose its prices to max...

We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors), which is a subclass of strongH-tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016) in some case. Based on this set, we give a checkable sufficient condition for the positive (semi...