This mograph deals with approximation and ise cancellation of dyn- ical systems which include linear and nlinear input/output relationships. It also deal with approximation and ise cancellation of two dimensional arrays. It will be of special interest to researchers, engineers and graduate students who have specialized in ?ltering theory and system theory and d- ital images. This mograph is composed of two parts. Part I and Part II will deal with approximation and ise cancellation of dynamical systems or digital images respectively. From iseless or isy data, reduction will be made. A method which reduces model information or ise was proposed in the reference vol. 376 in LNCIS [Hasegawa, 2008]. Using this method will allow model description to be treated as ise reduction or model reduction without having to bother, for example, with solving many partial di?er- tial equations. This mograph will propose a new and easy method which produces the same results as the method treated in the reference. As proof of its advantageous e?ect, this mograph provides a new law in the sense of numerical experiments. The new and easy method is executed using the algebraic calculations without solving partial di?erential equations. For our purpose,manyactualexamplesofmodelinformationandisereductionwill also be provided. Using the analysis of state space approach, the model reduction problem may have become a major theme of techlogy after 1966 for emphasizing e?ciency in the ?elds of control, ecomy, numerical analysis, and others.
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Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg, Springer-Verlag Berlin and Heidelberg Gmbh & Co. K