We present efficient implement at ions of the balanceand-truncate model reduction technique for large-scale systems. The key observation that distinguishes our approach is that Krylov subspace methods (Arnoldi and Lanczos) directly yield approximate low-rank square roots1 of the system Gramians; the balancing transformation can be then constructed from these square roots, obviating the need for...

In this paper, we propose the least-squares method for computing the positive solution of a m × n fully fuzzy linear system (FFLS) of equations, where m > n, based on Kaffman’s arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of the non...

In this paper, a new method based on parametric form for approximate solu-tion of fuzzy linear matrix equations (FLMEs) of the form AX = B; where Ais a crisp matrix, B is a fuzzy number matrix and the unknown matrix X one,is presented. Then a numerical example is presented to illustrate the proposedmodel.

Binary symmetry constraints of the N -wave interaction equations in 1 + 1 and 2 + 1 dimensions are proposed to reduce the N -wave interaction equations into finite-dimensional Liouville integrable systems. A new involutive and functionally independent system of polynomial functions is generated from an arbitrary order square matrix Lax operator and used to show the Liouville integrability of th...