Random Sampling of Moment Graph: A Stochastic Krylov-Reduction Algorithm

In this paper we introduce a new algorithm for model order reduction in the presence of parameter or process variation. Our analysis is performed using a graph interpretation of the multi-parameter moment matching approach, leading to a computational technique based on Random Sampling of Moment Graph (RSMG). Using this technique, we have developed a new algorithm that combines the best aspects of recently proposed parameterized moment-matching and approximate TBR procedures. RSMG attempts to avoid both exponential growth of computational complexity and multiple matrix factorizations, the primary drawbacks of existing methods, and illustrates good ability to tailor algorithms to apply computational effort where needed. Industry examples are used to verify our new algorithms.