Zusammenfassung
Many important problems in applied sciences, mathematics, and engineering can be
reduced to matrix problems. Moreover, various applications often introduce a special
structure into the corresponding matrices, so that their entries can be described by a
certain compact formula. Classic examples include Toeplitz matrices, Hankel matrices,
Vandermonde matrices, Cauchy matrices, Pick matrices, Bezoutians, controllability and
observability matrices, and others. Exploiting these and the more general structures often
allows us to obtain elegant solutions to mathematical problems as well as to design more
efficient practical algorithms for a variety of applied engineering problems.
Structured matrices have been under close study for a long time and in quite diverse (and
seemingly unrelated) areas, for example, mathematics, computer science, and engi-
neering. Considerable progress has recently been made in all these areas, and especially
in studying the relevant numerical and computational issues. In the past few years, a
number of practical algorithms blending speed and accuracy have been developed. This
significant growth is fully reflected in these volumes, which collect 38 papers devoted to
the numerous aspects of the topic.
The collection of the contributions to these volumes offers a flavor of the plethora of
different approaches to attack structured matrix problems. The reader will find that the
theory of structured matrices is positioned to bridge diverse applications in the sciences
and engineering, deep mathematical theories, as well as computational and numerical
issues. The presentation fully illustrates the fact that the techniques of engineers, mathe-
maticians, and numerical analysts nicely complement each other, and they all contribute
to one unified theory of structured matrices.
The book is published in two volumes. The first contains articles on interpolation, system
theory, signal and image processing, control theory, and spectral theory. Articles in the
second volume are devoted to fast algorithms, numerical and iterative methods, and
various applications.
Nutzer