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Abstract: In this paper, we first give the existence of and the general expression for the solution to an inverse eigenproblem defined as follows: given a set of real -vectors and a set of real numbers , and an -by- real generalized reflexive matrix (or generalized anti-reflexive matrix ) such that and are the eigenvectors and eigenvalues of (or ), respectively, we solve the best approximation problem for the inverse eigenproblem. That is, given an arbitrary real -by- matrix , we find a matrix which is the solution to the inverse eigenproblem such that the distance between and is minimized in the Frobenius norm. We give an explicit solution and a numerical algorithm for the best approximation problem over generalized reflexive (or generalized anti-reflexive) matrices. Two numerical examples are also presented to show that our method is effective. [ABSTRACT FROM AUTHOR]