内积空间上最小二乘形式的矩阵Pade-型逼近

Least-squares Matrix Padé-Type Approximation in the Inner Product Space

当矩阵幂级数的展开式的系数产生微小摄动时,矩阵Padé-型逼近解往往变化很大.本文在矩阵Padé-型逼近研究的基础上,受Brezinski的启发,借助于误差公式和最小二乘法构造了一种稳定性和精确度均有所提高的矩阵Padé-型逼近的新方法,即最小二乘形式的矩阵Padé-型逼近(LSMPTA),并给出了LSMPTA完整的分子和分母行列式表达式.最后,通过数值实例说明了这一方法的有效性.

Matrix Padé-type approximation can be quite sensitive to perturbation on the coefficients of the power series.In this paper,a new matrix Padé-type approximation （LSMPTA） is constructed by means of error formula and least-squares method,which is more stable and accurate.The idea of this construction is partly derived from Claude Brezinski.The numerator and denominator of LSMPTA determinant expressions are given.In the end,an example given shows that the method is effective.