Stanimirovic Computation of Generalized Matrix Inverses and Applications

Erscheinungsjahr 2017
ISBN: 978-1-351-63005-4
Verlag: Taylor & Francis
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 292 Seiten

Computation of General Matrix Inverses and Applications offers a gradual exposition to matrix theory as a subject of linear algebra. It presents both the theoretical results in generalized matrix inverses and the applications. The book is as self-contained as possible, assuming no prior knowledge of matrix theory and linear algebra.

The book first addresses the basic definitions and concepts of an arbitrary generalized matrix inverse with special reference to the calculation of {i,j,.,k} inverse and the Moore-Penrose inverse. Then, the results of LDL* decomposition of the full rank polynomial matrix are introduced, along with numerical examples. Methods for calculating the Moore-Penrose’s inverse of rational matrix are presented, which are based on LDL* and QDR decompositions of the matrix. A method for calculating the A(2)T;S inverse using LDL* decomposition using methods is derived as well as the symbolic calculation of A(2)T;S inverses using QDR factorization.

The text then offers several ways on how the introduced theoretical concepts can be applied in restoring blurred images and linear regression methods, along with the well-known application in linear systems. The book also explains how the computation of generalized inverses of matrices with constant values is performed, and covers several methods, such as methods based on full-rank factorization, Leverrier-Faddeev method, method of Zhukovski, and variations of partitioning method.

Autoren/Hrsg.

Stanimirovic, Ivan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Zahlensysteme
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Introduction

Computing Generalized Inverses of Matrices with Numerical Values

Generalized Inverses of Polynomial and Rational Matrices

Applications

Conclusion

Literature

Über Autor(innen)

Ivan Stanimirovic, PhD, is currently with the Department of Computer Science, Faculty of Sciences and Mathematics at the University of Niš, Serbia, where he is an Assistant Professor. He formerly was with the Faculty of Management at Megatrend University, Belgrade, as a Lecturer. His work spans from multi-objective optimization methods to applications of generalized matrix inverses in areas such as image processing and restoration and computer graphics. His current research interests include computing generalized matrix inverses and its applications, applied multi-objective optimization and decision making, as well as deep learning neural networks. Dr. Stanimirovic was the Chairman of a workshop held at 13th Serbian Mathematical Congress, Vrnjacka banja, Serbia, in 2014.