Approximation of Large-ScaleDynamical Systems

摘要

As our understanding of a given phenomenon increases, thequestions we may ask become more complex.This usually means that more details of thenatural world are taken into account as we attempt toinclude them in the model we are investigating. Atsuch a stage, if not earlier, our only recourse is toperform computations, and these become granderand more intricate as time and understanding moveon. Moreover, the fruitful interactions which occurat the boundaries of traditional scientific disciplinesmay often be mediated by mathematicians, but thenon-mathematicians usually want as many details aspossible to be included in any resulting computations. This bookaddresses the question of how to take good approximations ofdetailed models, when issues of limited computational, accuracy,and storage capacities come into play. This is the book's centraltheme of model reduction, formulated in the foreword as follows:"Given a linear time-invariant input/output system defined bythe convolution integral, a transfer function, a state space repre-sentation, or their discrete-time counterparts, approximate thissystem by a simpler system." Essentially, the choice reduceseither to minimising complexity at the expense of accuracy(so-called "misfit"), or minimising misfit at the expense ofcomplexity.