Fast singular-value decomposition of Loewner matrices for state-space macromodeling

Computation of a singular-value decomposition (SVD) of a Loewner matrix is an essential step in several frequency-domain macromodeling algorithms. When the data set is large, the computational cost of this step is prohibitive. We describe a fast algorithm that avoids explicitly forming the Loewner matrix. Instead, it exploits the matrix´s structure and rapid decay of singular values in typical applications to compute only the dominant singular values and corresponding singular vectors. A robust stopping criterion ensures accurate results up to a given tolerance. Computation times of less than two minutes are reported for matrices with as many as 10⁵ rows and columns.