Has the Function Relationship of the Four Diagonal Matrix Inverse Eigenvalue Problem of the Algorithm

Abstract

Matrix eigenvalue problems frequently encountered in many fields of mathematics and science and technology, is one of the core subject of numerical algebra, its research has important theoretical significance and application value. Our study is determined by eigenvalue and eigenvector of the matrix elements, known as the matrix inverse eigenvalue problem. The problem is ill-posed, so need to add some restrictive conditions. Therefore, matrix inverse eigenvalue problem is under certain conditions, according to the information to determine matrix eigenvalue and eigenvector of the elements. In this paper, we study on the condition of a given eigenvalue and eigenvector down backward four diagonal matrix problem. This paper discusses the existence and uniqueness of the solution, given the solution algorithm, and provides a numerical example.