The idea for this book originated during the workshop "Model order
reduction, coupled problems and optimization" held at the Lorentz Center
in Leiden from S- tember 19-23, 2005. During one of the discussion
sessions, it became clear that a book describing the state of the art in
model order reduction, starting from the very basics and containing an
overview of all relevant techniques, would be of great use for students,
young researchers starting in the ?eld, and experienced researchers. The
observation that most of the theory on model order reduction is
scattered over many good papers, making it dif?cult to ?nd a good
starting point, was supported by most of the participants. Moreover,
most of the speakers at the workshop were willing to contribute to the
book that is now in front of you. The goal of this book, as de?ned
during the discussion sessions at the workshop, is three-fold: ?rst, it
should describe the basics of model order reduction. Second, both
general and more specialized model order reduction techniques for linear
and nonlinear systems should be covered, including the use of several
related numerical techniques. Third, the use of model order reduction
techniques in practical appli- tions and current research aspects should
be discussed. We have organized the book according to these goals. In
Part I, the rationale behind model order reduction is explained, and an
overview of the most common methods is described.