求解分块循环三对角方程组的新算法  

NEW ALGORITHM OF SOLVING CIRCULANT BLOCK TRIDIAGONAL SYSTEMS

作　　者：卢学飞[1] 徐仲[2] 陆全[2] 安晓虹[2] 

机构地区：[1]西安石油大学理学院,西安710065 [2]西北工业大学应用数学系,西安710072

出　　处：《数值计算与计算机应用》2007年第4期275-281,共7页Journal on Numerical Methods and Computer Applications

基　　金：陕西省自然科学基金(2004CS110002)资助

摘　　要：分块循环三对角方程组的求解在科学与工程计算中有着广泛的应用.本文根据分块循环三对角矩阵的特殊分解,给出了求解分块循环三对角方程组的一种新算法.该算法含有可以选择的参数矩阵,适当选择这些参数矩阵,可以使得计算精度高于追赶法,甚至当追赶法失效时,由该算法仍可得到一定精度的解.而数值算例的结果与理论分析的结果也吻合.A new algorithm of solving circulant block tridiagonal systems is proposed, which is based on the special factorization of circulant block tridiagonal matrix. The algorithm in- cludes selective parameter-matrices. Proper selected parameter-matrices make new algo- rithm higher in precision and time than the famous Thomas algorithm. When the Thomas algorithm invalidate for some numerical examples, the new algorithm can solve.The analytic results match closely with the Results measured from the numerical examples.

关 键 词：分块循环三对角矩阵 追赶法 参数矩阵 

分 类 号：O241[理学—计算数学]