A Fast Recursive Algorithm for Constructing Matrices with Prescribed Eigenvalues and Singular Values

The Weyl Horn theorem characterizes a relationship between the eigenvalues and the singular values of an arbitrary matrix Based on that charac terization a fast recursive algorithm is developed to construct numerically a matrix with prescribed eigenvalues and singular values Beside being theoretically interest ing the technique could be employed to create test matrices with desired spectral features Numerical experiment shows this algorithm is quite e cient and robust