Fast Similarity Factorization for Solving Matrix Dynamic Equation

Abstract

This paper proposes a new method for solving the inversion of the system matrix that appears in the process of numerical integration of matrix dynamic equation. The singular value decomposition (SVD) has been widely known to solve the inversion of the matrix or to solve the Riccatti type matrix equation. The prominent advantage of using the SVD method resides in the fact that it provides singular values of the system matrix. However its low convergence rate hampers it to be used in the applications that handle a large-scale system matrix or in the real time control. The fast similarity factorization (FSF) proposed in this paper is one kind of SVD in a sense that it consists of many times orthogonal transformations. But the FSF provides fast and stable singular value decomposition. The simulation shown in this paper reveals its overwhelming convergence rate compared to the conventional SVD algorithms.