关键词: 二元齐次, Padé-型逼近, 递推算法, 矩阵形式幂级数, 正交多项式

Abstract: With appropriate variable replacement, the bivariate homogeneous matrix formal power series is transformed to univariate matrix formal power series with parameters. The bivariate homogeneous matrix Padé-type approximation was defined. To improve computation accuracy, using an error formula, the numerator and denominator in the determinant expressions of bivariate homogeneous matrix orthogonal polynomial Padé-type approximation are given based on the matrix E_MN. A Sylvester-type recursive algorithm is presented to avoid computation of high degree determinants. A numerical example shows effectiveness of the algorithm.

Key words: bivariate homogeneous, iterative algorithm, matrix formal power series, orthogonal polynomial, Padé-type approximation