A fast recursive algorithm for constructing matrices with prescribed eigenvalues and singular values. (English) Zbl 0994.65040
Summary: The Weyl-Horn theorem characterizes a relationship between the eigenvalues and the singular values of an arbitrary matrix. Based on that characterization, a fast recursive algorithm is developed to construct numerically a matrix with prescribed eigenvalues and singular values. Besides being of theoretical interest, the technique could be employed to create test matrices with desired spectral features. A numerical experiment shows this algorithm to be quite efficient and robust.
MSC:
65F18 | Numerical solutions to inverse eigenvalue problems |
15A42 | Inequalities involving eigenvalues and eigenvectors |