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 10
⁵
rows and columns.