In this paper, we first consider the existence of and the general expression for thesolution to the constrained inverse eigenproblem defined as follows: given a set of complex n-vectorsfxigmi=1 and a set of complex numbers f¸igmi=1, and an s-by-s real matrix C0, find an n-by-n realcentrosymmetric matrix C such that the s-by-s leading principal submatrix of C is C0, and fxigmi=1and f¸igmi=1 are the eigenvectors and eigenvalues of C respectively. We then concerned with the bestapproximation problem for the constrained inverse problem whose solution set is nonempty. Thatis, given an arbitrary real n-by-n matrix ˜ C, find a matrix C which is the solution to the constrainedinverse problem such that the distance between C and ˜ C is minimized in the Frobenius norm. We givean explicit solution and a numerical algorithm to the best approximation problem. Some illustrativeexperiments are also presented.
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