Thiele-type and Lagrange-type generalized inverse rational interpolation for rectangular complex matrices

Abstract

A variety of matrix rational interpolation problems include the partial realization problem for matrix power series and the minimal rational interpolation problem for general matrix functions. Different from the previous work, in this paper we consider a new method of matrix rational interpolation, with rectangular real or complex interpolated matrices and distinct real or complex interpolation points. Based on an axiomatic definition for the generalized inverse matrix rational interpolants (GMRI), GMRI are constructed in the following two forms: (i) Thiele-type continued fraction expression; (ii) an explicit determinantal formula for the denominator scalar polynomials and for the numerator matrix polynomials, which are of Lagrange-type expression. As a direct application of GMRI, a matrix rational extrapolation is introduced.