Structured Matrices in Mathematics, Computer Science, and Engineering II

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. 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 engineering. In this book, the author provides an interplay between the techniques of engineers and mathematicians and offers a flavor of the plethora of different approaches to attack structured matrix problems. Here, the reader will find that the theory of structured matrices is positioned to bridge diverse applications in the sciences and engineering, deep mathematical theories, and computational and numerical issues. Considerable progress has recently been made in studying relevant numerical issues to the topic. And in the past few years, a number of algorithms blending speed and accuracy have been developed. This significant growth is fully reflected in this volume, which collects 38 papers devoted to the numerous aspects of the topic employing myriad techniques. Readers will enjoy a full measure of different problems, different focuses, and different methods---all contributing 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.