对称次反对称三对角矩阵反问题  

The inverse problems of symmetric and skew-anti-symmetric tridiagonal matrices

作　　者：易福侠[1] 王金林[2] 袁达明[2] 

机构地区：[1]南昌航空大学科技学院基础课部,江西南昌330034 [2]南昌航空大学数学与信息科学学院,江西南昌330063

出　　处：《济南大学学报（自然科学版）》2015年第2期151-160,共10页Journal of University of Jinan(Science and Technology)

基　　金：国家自然科学基金(AA201207156);江西省教改课题专项(JXJG-13-36-2)

摘　　要：引入对称次反对称三对角阵向量对反问题,利用对称次反对称矩阵的性质和线性方程组Ax=b有解的条件,得到了所研究问题有唯一解的充要条件及解的表达式。最后给出了求解问题的数值算法和数值例子。The inverse problems of vector pairs for symmetric and skew-anti-symmetric tridiagonal matrices are introduced,and some necessary and sufficient conditions under which there exist unique solutions for the discussed problems and the expressions of solutions are obtained by using the properties of symmetric and skew-anti-symmetric matrices and the conditions for the solvability of the linear system Ax = b. Finally the numerical algorithms and examples to solve the problems are also given.

关 键 词：反问题 对称次反对称矩阵 向量对 线性方程组 三对角矩阵 

分 类 号：O241.6[理学—计算数学]