ABSTRACT

This chapter considers algorithms for computing generalized inverses of polynomial and rational matrices. It discusses some applications of generalized inverses of constant, rational, and polynomial matrices. Symbolic calculation of generalized inverse is usually performed through the decomposition of the full-rank appropriate matrix. Motivation is derived from the benefits of using free-roots decomposition in the algorithms for polynomial and rational matrices. In this way, the difficulties of calculating symbolic polynomial matrices and their inverses, arising from the emergence of elements with roots are avoided. Obviously sometimes coefficients of the polynomial can be a growth in inter-steps, even though simplification is executed. One possible solution to this problem is to consider implementation large number operations. Polynomial implementation is implemented in by using a series of coefficients. The motivation is to use no decomposition algorithm to obtain root for the calculation of Moore-Penrose's inverse rational matrix.