A new criterion for the H-matrix property

Diagonal dominance, Schur complements and some classes of H-matrices and P-matrices

“…However, for large sparse matrices, it is more convenient the use of iterative methods for this purpose as well as for the construction of D. This is an important recent field of research and has been studied in the last years (cf. [1][2][3][10][11][12]). In these papers, the practical interest and applications of this subject is shown, as well as its difficulty.…”

“…[1][2][3][10][11][12]). Given a matrix A = (a ij ) 1≤i, j≤n and the numbers r i (A) of (2.1), let us define the following subset of indices of {1, 2, .…”

An extended compact profile iterative method criterion for sparse H-matrices

“…An H -matrix (usually A ∈ C n,n ) is closely related to an M-matrix and many convergence properties of an M-matrix carry over, almost directly, to convergence properties for an H -matrix. This explains the fact that in the last decade so many works ( [2][3][4][5]7,9,11,12]) have appeared to propose various criteria (algorithms) that decide whether the matrix A of the linear system to be solved is an H -matrix. The majority of the criteria to make this decision are iterative in nature and assume, without explicitly stating it, that the matrix A in question is dense.…”

“…In Section 3, we describe analytically the background of the algorithmic material that is used for the extension of a modification of the technique in [8]. In Section 4, the three parts of an algorithm, that has as a starting point the one in [11] and is also based on minor elements from other works ( [12], etc. ), are presented.…”

Criteria and Schur complements of H-matrices

“…A strictly generalized diagonally dominant matrix is nothing but an H -matrix (see [1, p. 185] or [9, p. 124]). Criteria and characterizations for H -matrices, denoted by H, are presented in [4,12,16,18,22,24]. Related studies have also been witnessed in [5,6,10,20,21].…”