An Improved Two-Step Method for Inverse Singular Value Problems

Based on the technique of T. Ogita and K. Aishima (2020) and J. A. Ezquerro and M. A. Hernández (2012), we designed an improved two-step method for solving the inverse singular value problems. Compared with other existing two-step methods, the proposed method has comparable computational cost. However, computing the product of matrices is simpler than solving linear equations and has no instability problem caused by ill-conditioning in solving linear equations, and thus it seems more stable and greatly reducing computational costs. Under appropriate assumptions, the proposed method is proved to be convergent with the cubic root-convergence rate. The proposed method is applied to the noise reduction for modal parameters estimation and indicates that it can significantly remove noise from measured signals and accurately estimate the modal frequencies and damping ratios. The numerical results demonstrate the effectiveness of the improved method.