A kind of the inverse eigenvalue problem for five-diagonal matrix

This paper presents a kind of the inverse eigenvalue problem for the real five-diagonal matrix: Given three real numbers unequal, three nonzero real vectors, another n-2 real numbers as well as the constant k. Find n order real five--diagonal matrices B, such that the establishment of three equations with matrix B and the known information. Where, B are the matrices with proportional relation on minor diagonal and the second minor diagonal. Another n-2 real numbers are the elements of the second minor diagonal in super-diagonal matrix. Discussed necessary and sufficient conditions of the unique solution of the existence, then the expression of the solution of the problem is given, and a numerical example is provided.