严格对角占优的对称块三对角矩阵的逆  

Inverse of Strictly Diagonally Dominant Symmetric Block Tridiagonal Matrices

作　　者：连培培 畅大为[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《烟台大学学报（自然科学与工程版）》2016年第1期14-17,共4页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(60671063)

摘　　要：为了研究严格对角占优的对称块三对角矩阵的逆,利用了转换矩阵产生的关于块的连续两届递归关系及矩阵的代数运算方法,在其求逆的原有的计算公式的基础上,给出了求解严格对角占优的对称块三对角矩阵的逆的一种新的数值算法,在计算复杂度上改进了现有的结果,并在文章最后利用数值算例验证了其有效性.To find a simpler and more accurate expression for the inverse of the symmetric block tridiagonal matrices,applying the recursive relations between blocks of two-consecutive-terms and algebraic operational method of matrices and the previous calculating formula of the inverse of the symmetric block tridiagonal matrices,we derive the new espression for the inverse of the symmetric block tridiagonal matrices. The new expression has more advantages in computational complexity than the one obtained previously. Finally,its validity is validated with a numerical example.

关 键 词：对称块三对角矩阵 严格对角占优矩阵 逆矩阵 算法 

分 类 号：O241.6[理学—计算数学]