A Fast Recursive Algorithm for Constructing Matrices with Prescribed Eigenvalues and Singular Values
Moody T. Chu · SIAM Journal on Numerical Analysis · 2000
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. Numerical experiment shows this algorithm to be quite efficient and robust.