A Band Lanczos Process Based on Coupled Recurrences with Applications in Model-Order Reduction

Zhaojun Bai

Department of Mathematics University of Kentucky Lexington, KY 40506


A new variant of the band symmetric Lanczos process will be present in this talk. The classical band Lanczos process successively reduces a given matrix A to nearly band (the ``fish-bone'') form T. In this new variant, a sparsity-structure persevered LDL^T factorization of T is directly computed provided the existence of such factorization. The motivation and application of this work stem from emerging model-order reduction techniques based on Lanczos process in large scale circuit simulation. Although the new band Lanczos process requires slight more arithmetic and storages, it makes theoretically proven passive reduced-order models passive in practice. Numerical examples demonstrate that it is far more robust and accurate than the previous ones. This is a joint work with Roland Freund at Bell Labs, Lucent Technologies.