The inverse eigenvalue problem for a bordered anti-tridiagonal matrix

The inverse matrix problem is a hot and active research topic in computational mathematics^[1]. It has broad applications in engineering and scientific calculation, and owns a strong background in physics and practical significance^[2]. This paper explores the inverse eigenvalue problem of a bordered anti-tridiagonal matrix. It first illustrates the existence and the uniqueness of its solution, the elaborates on the recursive expression of the solution and uses one numerical example to show the effectiveness of the algorithm, and finally concludes that this work is significant and points out suggestions for further study.