The Inverse Eigenvalue Problem of Tridiagonal Matrix with Proportional Relationships

The matrix eigenvalue inverse problem is the problem of inversely determining the matrix by using the information of the known eigenvalues and eigenvectors and other constraints. The matrix eigenvalue inverse problem is not only deeply studied in the field of mathematics, but also in other engineering fields Both have a very wide range of applications. This paper studies the inverse eigenvalue problem of a class of tridiagonal matrices with proportional relationships, constructs a matrix by given two eigenpairs, and obtains an algorithm for inverting the matrix. At the same time, the corresponding. The uniqueness theorem of, and the validity of the algorithm is verified by numerical examples.