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"This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field.The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered.This book is not merely a collection of articles. The editors have gone to considerable lengths to blend the individual papers into a consistent presentation. Each chapter exposes the reader to some of the most recent research while providing enough background material to put the work into proper context."

"This book provides a comprehensive treatment of the theory of polynomials in a complex variable with matrix coefficients. Basic matrix theory can be viewed as the study of the special case of polynomials of first degree; the theory developed in Matrix Polynomials is a natural extension of this case to polynomials of higher degree. It has applications in many areas, such as differential equations, systems theory, the Wieneropf technique, mechanics and vibrations, and numerical analysis. Although there have been significant advances in some quarters, this work remains the only systematic development of the theory of matrix polynomials."

"This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge. Covering everything from classic results to the most recent developments, Spectral Properties of Banded Toeplitz Matrices is an important resource. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded ones until now has primarily been found in research papers."

"Sebuah graf dengan simpul dapat direpresentasikan sebagai matriks simetris berukuran nxn seperti matriks ketetanggaan dan laplacian. Matriks simetris dijamin oleh teorema spektral, memiliki nilai eigen lengkap (ruang eigen setara dengan R^n). Hal ini memberikan kemungkinan untuk menelaah sifat graf dengan menggunakan nilai eigen dan vektor eigen matriks ketetanggaan dan laplacian. Himpunan nilai eigen beserta multiplisitasnya disebut sebagai spektrum. Pada skripsi ini dibahas tentang sifat dari spektrum matriks ketetanggaan dari graf teratur yang diasosiasikan pada nilai eigen terbesarnya serta sifat dari spektrum matriks laplacian dari graf teratur yang diasosiasikan pada rata-rata nilai eigen. Selanjutnya, juga dibahas keterhubungan antara spektrum matriks laplacian dan ketetanggaan pada graf reguler.

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A graph with vertices can be represented as a symmetric matrix of size nxn, such as an adjacency matrix and Laplacian matrix. Symmetric matrices, guaranteed by the spectral theorem, have a complete eigenvalue (eigenspace equal to R^n). This provides ways to learn graphs using eigenvalues and eigenvectors of their adjacency and laplacian matrices. A spectrum is a set of eigenvalues together with their multiplisities. This thesis discuss the properties of the spectrum of the adjacency matrix of regular graphs associated with their largest eigenvalue, as well as the properties of the spectrum of the Laplacian matrix of regular graphs associated with the average eigenvalue. Subsequently, the interrelation between the spectra of the laplacian and adjacency matrices in regular graphs will be examined."