Abstract: In terms of the recursive relation in the Lagrange polynomial form, a method of Lagrange-type matrix rational interpolation is presented in the inner product space. When all interpolation points approach zero, a matrix Pad
é approximation with chosen coefficients is constructed, whose coefficients can be obtained by the least square method. An error formula of the matrix Padé approximation is given.

Key words: Lagrange polynomial, rational interpolation, matrix Padé approximation, matrix-valued