基于正交投影方法的二次特征值反问题及其最佳逼近解
发布时间：2018-12-18 09:46
【摘要】：考虑二次特征值反问题的广义中心对称解(广义反中心对称解)及其最佳逼近问题,应用矩阵的正交投影方法,给出矩阵方程AX+BY+CZ=0的解及其最佳逼近问题.利用广义中心对称矩阵(广义反中心对称矩阵)的性质导出了该问题有广义中心对称解(广义反中心对称解)的条件及有解情况下的通解表达式,并证明了最佳逼近问题解的存在性与唯一性,得到了最佳逼近解的表达式.
[Abstract]:In this paper, we consider the generalized centrosymmetric solution (generalized anti-centrosymmetric solution) and its best approximation problem of inverse quadratic eigenvalue problem. By using the orthogonal projection method of matrix, we give the solution of matrix equation AX BY CZ=0 and its best approximation problem. By using the properties of generalized centrosymmetric matrix (generalized anti-centrosymmetric matrix), the conditions for the problem with generalized centrosymmetric solution (generalized anti-centrosymmetric solution) and the general solution expression for the problem with solutions are derived. The existence and uniqueness of the solution of the best approximation problem are proved, and the expression of the best approximation solution is obtained.
【作者单位】： 东北电力大学理学院;
【基金】：国家自然科学基金(批准号:11072085) 吉林省自然科学基金(批准号:201115180)
【分类号】：O241.6
[Abstract]:In this paper, we consider the generalized centrosymmetric solution (generalized anti-centrosymmetric solution) and its best approximation problem of inverse quadratic eigenvalue problem. By using the orthogonal projection method of matrix, we give the solution of matrix equation AX BY CZ=0 and its best approximation problem. By using the properties of generalized centrosymmetric matrix (generalized anti-centrosymmetric matrix), the conditions for the problem with generalized centrosymmetric solution (generalized anti-centrosymmetric solution) and the general solution expression for the problem with solutions are derived. The existence and uniqueness of the solution of the best approximation problem are proved, and the expression of the best approximation solution is obtained.
【作者单位】： 东北电力大学理学院;
【基金】：国家自然科学基金(批准号:11072085) 吉林省自然科学基金(批准号:201115180)
【分类号】：O241.6
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