一种求解病态复线性方程组的混合算法

A Hybrid Algorithm of Ill-conditioned Complex Linear Equations

病态复线性方程的求解是现代应用数学和很多工程应用面临的难题,用一般算法进行求解时,得到的误差较大,因此在一些高精度的工程应用上,其结果往往不是特别理想。而随着科技的发展,现代很多工程应用对数据具有越来越高的精度要求(尤其是国家航天航空),因此一个能求解病态复线性方程组的高精度算法是很有必要的。从病态复线性方程组求解的特点出发,对模拟退火法进行改进,并将其全局的收敛能力与双共轭梯度法的高精度求解能力结合起来,提出了一种BCG-SA混合算法。数据实验表明,模拟退火法能对双共轭梯度法求出的解进行微调动,帮助双共轭梯度法在概率意义上跳出局部极小值点,从而提高求解精度。

Solving ill-conditioned complex linear equations is difficult in modem applied mathematics and many engineering application, and it is easy to produce significant error and bad result for general algorithms in some high-accuracy application with a usual algorithm. With the development of science and technology, there is more and more restrictions on data accuracy for modem industry especially space flight and aviation. Therefore,it is necessary and impending to find a high accuracy algorithm for ill-conditioned complex linear e- quations. According to the characteristics of ill-conditioned complex linear equations, a hybrid algorithm of BCG-SA improved with sim- ulated annealing algorithm has been proposed with the advantages of global convergence and high precision solution for bi-conjugate gra- dient algorithm. The experimental results show that the hybrid algorithm has promoted the precision of solution for bi-conjugate gradient algorithm which can jump out of the neighborhoods of local minimum points in the sense of probability.