MATRIX ALGORITHMS AND ERROR FORMULA FOR BIVARIATE THIELE-TYPE RECTANGULAR MATRIX VALUED RATIONAL INTERPOLATION

A new method for the construction of bivariate matrix valued rational interpolants (BGIRI) on a rectangular grid is presented in [6]. The rational interpolants are of Thiele-type continued fraction form with scalar denominator. The generalized inverse introduced by [3]is generalized to rectangular matrix case in this paper. An exact error formula for interpolation is obtained , which is an extension in matrix form of bivariate scalar and vector valued rational interpolation discussed by Siemaszko[12] and by Gu Chuangqing [7] respectively. By defining row and column-transformation in the sense of the partial inverted differences for matrices, two type matrix algorithms are established to construct corresponding two different BGIRI, which hold for the vector case and the scalar case.