A stable test for checking if a matrix is a nonsingular M -matrix is presented. Its computational cost is, in the worst case, O(n2) elementary operations higher than the computational cost of Gaussian elimination. The test can be applied to check if a nonnegative matrix has spectral radius less than 1.

None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX +BX +C = 0 with square matrices A,B, C and X, can provide an exact solution; they can just obtain approximations to an exact solution. We use interval arithmetic to compute an interval matrix which contains an exact solution to this quadratic matrix equation, where we aim at obtaining na...

None of the usual floating point numerical techniques available for solving the quadratic matrix equation AX +BX +C = 0 with square matrices A,B, C and X, can provide an exact solution; they can just obtain approximations to an exact solution. We use interval arithmetic to compute an interval matrix which contains an exact solution to this quadratic matrix equation, where we aim at obtaining na...

A unifying approach is presented between similarity, consimilarity, T congruence and *congruence of a matrix A to a symmetric, to a Hermitian or to a real matrix. Also studied are similarity consimilarity, T congruence and *congruence of a matrix A to A∗, AT , and A. Attempts are made to find special (con)similarities and congruences, as well as to find connections between these classes of maps...

A preconditioned SSOR iterative method with a multi-parameters preconditioner I + S̃α is proposed. Some convergence and comparison results for αi ∈ [0, 1] are given when the coefficient matrix of linear system A is a nonsingular M−matrix. Numerical example shows that our methods are superior to the basic SSOR iterative method.

The concept of a singular M-matrix A with respect to a proper cone X is extended, by replacing the usual regularity condition A = al B for a Xnonnegative matrix B with the weaker condition, exponential nonnegativity of A. As in earlier work which dealt with the nonsingular case, in the present characterizations the lack of regularity is overcome by employing subtangentiality.

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as...

In this paper, based on the structure of pentadiagonal CUPL-Toeplitz matrix and Sherman–Morrison–Woodbury formula, we develop a new algorithm for solving nonsingular linear system. Some numerical examples are given in order to illustrate effectiveness proposed algorithms.

Let L(λ) = Inλ m + Am−1λm−1 + · · ·+ A1λ + A0 be an n× n monic matrix polynomial, and let CL be the corresponding block companion matrix. In this note, we extend a known result on scalar polynomials to obtain a formula for the polar decomposition of CL when the matrices A0 and Pm−1 j=1 AjA ∗ j are nonsingular.