§1.引言 本文讨论下述特征值反问题的可解性: 问题 G.设A_0=(a_(ij)^((0)))和A_k=(a_(ij)^((k)))(k=1,…,n)是一组n+1个n×n实对称矩阵,λ_1,…,λ_n是n个不同的实数.求实数c_1,…,c_n使得矩阵A_0+sum from k-1 to n C_k·A_k的特征值为λ_1,…,λ_n. [1]和[2]曾给出此问题可解的充分条件.本文应用Rothe不动点定理[3]给出问题G可解的另外两个充分条件.
It is proved that the additive inverse eigenvalue problem is equivalent to a polynomial system. By studying the system we obtain some new sufficient conditions on the solvabitity, and some numerical methods. Some numerical examples are presented.
We study the Hermitian positive definite solutions of the matrix equation X +A*X^-qA = I with q > 0. Some properties of the solutions and the basic fixed point iterations for the equation are also discussed in some detail. Some of results in [Linear Algebra Appl., 279 (1998), 303-316], [Linear Algebra Appl., 326 (2001),27-44] and [Linear Algebra Appl. 372 (2003), 295-304] are extended.
