摘要
基于广义逆矩阵Ｐａｄｅ逼近的特点是在保持逼近阶的前提下，在构造过程中不需要用到矩阵的乘法运算．利用该结果建立矩阵指数ｅｔＡ的一种新的非线性逼近算法．该方法与原Ｐａｄｅ近似法相比具有明显的优点，即它对奇异矩阵和高阶矩阵是适用的，并且所得到的算法适合编程上机进行计算．给出的一个计算实例说明了算法的有效性．逼近公式的存在性和唯一性得到了证明．
The matrix Pade approximants based on generalized inverse is characterized by keeping approximation order and without multiplication of matrices in the construction process. In this paper, a new nonlinear approximating method for matrix exponential functions is established by means of this result. This method is obviously superior to the original Pade method because it can be applied to singular matrices and higher order matrices, and the obtained algorithm is suitable to compute on computers. A computational example is given to illustrate the efficiency of the algorithm. Existence and uniqueness of approximation formulas are proven.
出处
《自动化学报》
EI
CSCD
北大核心
1999年第1期94-99,共6页
Acta Automatica Sinica
基金
国家自然科学基金
