In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems where fuzzy coefficient matrix is a positive matrix. This paper mainly discusses a new decomposition of a nonsingular fuzzy matrix, a symmetric matrix times to a triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy s...

We consider applying the preconditioned conjugate gradient (PCG) method to solve linear systems Ax = b where the matrix A comes from the discretization of second-order elliptic operators. Let (L +)) ?1 (L t +) denote the block Cholesky factorization of A with lower block triangular matrix L and diagonal block matrix. We propose a preconditioner M = (^ L +)) ?1 (^ L t +) with block diagonal matr...

First, we give a new example of silting-discrete algebras. Second, one explores when the algebra triangular matrices over finite dimensional is τ-tilting finite. In particular, classify algebras which matrix are Finally, investigate silting-discrete.

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

In this work, the notion of extended eigenvalues a 2 ? lower triangular operator matrix has been researched. More precisely, relations between spectrum with spectrum, point and its diagonal entries have investigated. The obtained results supplemented by examples. addition, some properties block matrices displayed.

The improved computation presented in this paper is aimed to optimize the neural networks learning process using Levenberg-Marquardt (LM) algorithm. Quasi-Hessian matrix and gradient vector are computed directly, without Jacobian matrix multiplication and storage. The memory limitation problem for LM training is solved. Considering the symmetry of quasi-Hessian matrix, only elements in its uppe...