Generalized inverse matrix Padé approximation on the basis of scalar products

Abstract

A new type of generalized matrix inverse is used to define the generalized inverse matrix Padé approximants (GMPA). GMPA is introduced on the basis of scalar product of matrices, with the form of matrix numerator and scalar denominator. It is different from the existing matrix Padé approximants in that it does not need multiplication of matrices in the construction process. Some algebraic properties are discussed. The representations of GMPA are provided with the following three forms: (i) the explicit determinantal formulas for the denominator scalar polynomials and the numerator matrix polynomials; (ii) ε-algorithm expression; (iii) Thiele-type continued fraction expression. The equivalence relations above three representations are proposed.