Low-rank approximation and model reduction.

摘要: The basic idea of model reduction is to represent a complex linear dynamical system by much simpler one. This may refer many different techniques, but in this dissertation we focus on projection-based systems. projection based the dominant eigen-spaces energy functions for ingoing and outgoing signals system. These are called Gramians can be obtained as solutions Stein equations. When matrices large sparse, it not obvious how compute efficiently these or their eigen-spaces. In fact, direct methods ignore sparsity equations not very attractive for parallelization. Their use then limited if state dimension N large. The complexity roughly O(N3) floating point operations they require about O(N2) words memory. This thesis provides some new ideas recursive time-varying systems well time-invariant We present three algorithms computation projection. These combine two classical — namely Balanced Truncation Krylov subspaces produce a low-rank approximation input/output map system. show practical relevance our results with real world benchmark examples. also second order Such have special structure which one wants preserve reduced model. adapt method such