Physical Sciences and Mathematics Commons^™

Error Estimation Of The Padé Approximation Of Transfer Functions Via The Lanczos Process, Zhaojun Bai, Qiang Ye

Mathematics Faculty Publications

Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix point of view. This approach simplifies the mathematical theory and derivation of the algorithm. Moreover, an explicit formulation of the approximation error of the PVL algorithm is given. With this error expression, one may implement the PVL algorithm that adaptively determines the number of Lanczos steps required to satisfy a prescribed error tolerance. …