On the Construction of Tridiagonal Symmetric Matrices From Three Vector Pairs

In this paper,the inverse problems of constructing the irreducible tridiagonal matrixes,Jacobi matrixes and negative Jacobi matrixes with given three vector pairs are discussed.In the method for solving these problems,the equivalent relations between these problems and linear equation systems are considered.By using the conditions for the solvability of the linear equation systems,some necessary and sufficient conditions under which there exists a unique solution for the discussed problems are obtained.Furthermore a numerical algorithm and numerical experiments are presented.