由谱数据构造一类伪Jacobi矩阵  

ON THE CONSTRUCTION OF A PSEUDO-JACOBI MATRIX FROM ITS SPECTRAL DATA

作　　者：孟纯军[1] 李晗 

机构地区：[1]湖南大学数学与计量经济学院,长沙410082

出　　处：《高等学校计算数学学报》2017年第3期193-199,共7页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目:压缩传感中CS矩阵的构造理论与信号重构的快速算法(11271117)

摘　　要：1引言 Jacobi矩阵是如下形状的对称三对角矩阵： Jn=（a1 b1 b1 a2 b2 b2 … … … an-1 bn-1 bn-1 an）其中bi〉0，Jacobi矩阵的来源非常广泛，如模型修复、振动方程、航空动力等[13].Jacobi矩阵的特征值问题以及相应的逆特征值问题是数值代数中的热点研究之一，In this paper we consider a class of inverse eigenvalue problem for pseudo-Jacobi matrices which concerns the reconstruction of a class of pseudo- Jacobi matrices with certain patterns that the signs of symmetric position element are opposite according to some given spectrum and the eigenvalues of the n- 1 order leading principal sub-matrix . Firstly we investigate the property of eigenvalues for this pseudo-Jacobi matrices. Then we present the necessary and sufficient conditions under which the problem is solvable. The representations of the general and unique solution are also discussed. Finally we provide an algorithm to calculate the solution of the problem when the solution is unique. Furthermore we give a numerical example to illustrate that the algorithm is feasible.

关 键 词：JACOBI矩阵 数据构造 逆特征值问题 对称三对角矩阵 振动方程 数值代数 航空动力 

分 类 号：O241.6[理学—计算数学]