Linear parameterized inverse eigenvalue problem of bisymmetric matrices

In this paper, we consider the linear parameterized inverse eigenvalue problem of bisymmetric matrices which is described as follows:Problem IGiven real bisymmetric matrices B0,B1,B2,…,Bn, and real numbers λ1⁎,λ2⁎,…,λn⁎, find values of c=(c1,c2,…,cn)T such that the eigenvalues of the matrixB(c)=B0+c1B1+c2B2+⋯+cnBn are precisely λ1⁎,λ2⁎,…,λn⁎.We first establish the structure of bisymmetric matrices. Based on the Newton-type iterative method, we then turn Problem I into the inverse eigenvalue problems of symmetric matrices with small sizes, and solve these problems. Finally, we present numerical examples to illustrate our results.