基于内积矩阵E_(uv)的最小二乘形式矩阵Padé-型逼近

Least-Squares Matrix-Valued Padé-Type Approximation Based on Inner Matrix E_(uv)

为提高求矩阵Padé-型逼近解的精确度,给出一种求解矩阵Padé-型逼近解的改进算法,即基于矩阵Euv的正交多项式Padé-型逼近算法.另外,当矩阵值幂级数展开式的系数产生微小摄动时,矩阵幂级数的Padé-型逼近解变化往往很大,借助误差公式、内积单位矩阵和最小二乘法构造一种稳定性和精确度均有所提高的最小二乘形式矩阵Padé-型逼近算法.最后,对这两种算法分别给出完整的分子和分母行列式表达式.

To obtain better results of matrix Padé-type approximation,an improved algorithm is given for the matrix Padé-type approximation,which is called an orthogonal polynomial algorithm of matrix Padé-type approximation based on the matrix Euv in the inner space.Matrix Padé-type approximation can be quite sensitive to perturbation to the coefficients of the power series.In order to fill this gap,a least-squares algorithm of matrix Padé-type approximation is constructed.The numerator and denominator of the two algorithms determinant expressions are given.