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In this paper, we develop a modified gradient based algorithm for solving matrix equations AXB + CXTD = F. Different from the gradient based method introduced by Xie et al., 2010, the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method. [ABSTRACT FROM AUTHOR]

We consider the following inverse eigenvalue problem: to construct a special kind of matrix (real symmetric doubly arrow matrix) from the minimal and maximal eigenvalues of all its leading principal submatrices. The necessary and sufficient condition for the solvability of the problem is derived. Our results are constructive and they generate algorithmic procedures to construct such matrices. [ABSTRACT FROM AUTHOR]