In this paper we define multiplication between intuitionistic fuzzy matrices (IFMs) and we derive the conditions for a block IFM to be regular. Also a method to find the generalized inverse of it with the help of the generalized inverses of the blocks of the original matrix is described. Again, it is shown that a block intuitionistic fuzzy matrix can be decomposed into an upper triangular idemp...

Abstract. This paper studies the problem of the computation of common infinity-norm Lyapunov functions. For a set of continuous-time LTI systems or discrete-time LTI systems whose system matrices are upper triangular form or lower triangular form, it is proved that there exist common infinity-norm Lyapunov functions for them. Then four algorithms of computing common infinity-norm Lyapunov funct...

The objective of this note is to prove, under certain technical conditions, that the top-Lyapunov exponent of a strictly stationary random sequence of block-triangular matrices is equal to the maximum of the top-Lyapunov exponents of its diagonal blocks. This study is partially motivated by a basic technical problem in the identification of GARCH processes. A recent extension of the above inher...

A tridiagonal matrix with entries given by square matrices is a block tridiagonal matrix; the matrix is banded if off-diagonal blocks are upper or lower triangular. Such matrices are of great importance in numerical analysis and physics, and to obtain general properties is of great utility. The blocks of the inverse matrix of a block tridiagonal matrix can be factored in terms of two sets of ma...

abstract. let mn;m be the set of n-by-m matrices with entries inthe field of real numbers. a matrix r in mn = mn;n is a generalizedrow substochastic matrix (g-row substochastic, for short) if re e, where e = (1; 1; : : : ; 1)t. for x; y 2 mn;m, x is said to besgut-majorized by y (denoted by x sgut y ) if there exists ann-by-n upper triangular g-row substochastic matrix r such thatx = ry . th...

We present a parallelization of Parlett s algorithm for computing arbitrary functions of upper triangular matrices The parallel algorithm preserves the numerical stability properties of the serial algorithm and is suitable for implementation on coarse grain parallel computers The algorithm ob tains a speedup of for matrices of size greater than as our analysis and actual implementation on a pro...