On constructing unit triangular matrices with prescribed singular values (Q1577403)

The purpose of this paper is to provide an efficient algorithm for computing a unit lower triangular \(n\times n\) matrix with prescribed singular values \(\sigma_1,\dots, \sigma_n\), where \(\Pi_i\sigma_i= 1\). The idea of the proposed algorithm is to construct a sequence of unitarily equivalent lower triangular matrices \(A_i\in \mathbb{R}^{n\times n}\), \(i= 1,\dots, n\) with diagonal matrix \(\text{diag}(\sigma_1,\sigma_2,\dots, \sigma_n)\), where \(\sigma_1,\sigma_2,\dots, \sigma_n\), are given singular values. Numerical properties of the proposed algorithm depend mainly on the accuracy of the singular value decomposition routine for a \(2\times 2\) triangular matrix. All computations were carried out in MATLAB.