Shivakumar / Sivakumar / Zhang Infinite Matrices and Their Recent Applications

1. Auflage 2016
ISBN: 978-3-319-30180-8
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 118 Seiten

This monograph covers the theory of finite and infinite matrices over the fields of real numbers, complex numbers and over quaternions. Emphasizing topics such as sections or truncations and their relationship to the linear operator theory on certain specific separable and sequence spaces, the authors explore techniques like conformal mapping, iterations and truncations that are used to derive precise estimates in some cases and explicit lower and upper bounds for solutions in the other cases.
Most of the matrices considered in this monograph have typically special structures like being diagonally dominated or tridiagonal, possess certain sign distributions and are frequently nonsingular. Such matrices arise, for instance, from solution methods for elliptic partial differential equations. The authors focus on both theoretical and computational aspects concerning infinite linear algebraic equations, differential systems and infinite linear programming, among others. Additionally, the authors cover topics such as Bessel’s and Mathieu’s equations, viscous fluid flow in doubly connected regions, digital circuit dynamics and eigenvalues of the Laplacian.

Zielgruppe

Research

Autoren/Hrsg.

Shivakumar, P.N.

Sivakumar, K.C.

Zhang, Yang

Inhaltsverzeichnis

Introduction.- Finite Matrices and their Nonsingularity.- Infinite Linear Equations.- Generalized Inverses: Real or Complex Field.- Generalized Inverses: Quaternions.- M-matrices over Infinite Dimensional Spaces.- Infinite Linear Programming.- Applications.