Castillo / Cobo / Jubete Orthogonal Sets and Polar Methods in Linear Algebra

Applications to Matrix Calculations, Systems of Equations, Inequalities, and Linear Programming
1. Auflage 2011
ISBN: 978-1-118-03114-8
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 440 Seiten, E-Book

Reihe: Wiley Series in Pure and Applied Mathematics

A unique, applied approach to problem solving in linearalgebra
Departing from the standard methods of analysis, this unique bookpresents methodologies and algorithms based on the concept oforthogonality and demonstrates their application to both standardand novel problems in linear algebra. Covering basic theory oflinear systems, linear inequalities, and linear programming, itfocuses on elegant, computationally simple solutions to real-worldphysical, economic, and engineering problems. The authors clearlyexplain the reasons behind the analysis of different structures andconcepts and use numerous illustrative examples to correlate themathematical models to the reality they represent. Readers aregiven precise guidelines for:
* Checking the equivalence of two systems
* Solving a system in certain selected variables
* Modifying systems of equations
* Solving linear systems of inequalities
* Using the new exterior point method
* Modifying a linear programming problem
With few prerequisites, but with plenty of figures and tables,end-of-chapter exercises as well as Java and Mathematica programsavailable from the authors' Web site, this is an invaluabletext/reference for mathematicians, engineers, applied scientists,and graduate students in mathematics.

Autoren/Hrsg.

Castillo, Enrique

Cobo, Angel

Jubete, Francisco

Pruneda, Rosa Eva

Inhaltsverzeichnis

LINEAR SPACES AND SYSTEMS OF EQUATIONS.
Basic Concepts.
Orthogonal Sets.
Matrix Calculations Using Orthogonal Sets.
More Applications of Orthogonal Sets.
Orthogonal Sets and Systems of Linear Equations.
CONES AND SYSTEMS OF INEQUALITIES.
Polyhedral Convex Cones.
Polytopes and Polyhedra.
Cones and Systems of Inequalities.
LINEAR PROGRAMMING.
An Introduction to Linear Programming.
The Exterior Point Method.
APPLICATIONS.
Applications.
Appendices.
References.
Index.

Über Autor(innen)

ENRIQUE CASTILLO is a professor in the Department of AppliedMathematics and Computational Science at the University ofCantabria, Spain. During 25 years of research and teaching, he haspublished hundreds of papers as well as 18 books. ANGEL COBO is anassociate professor in the Department of Applied Mathematics andComputational Science in the University of Cantabria.
FRANCISCO JUBETE is a civil engineer and research assistant in theDepartment of Applied Mathematics and Computational Science at theUniversity of Cantabria.
ROSA EVA PRUNEDA is a research assistant in the Department ofApplied Mathematics and Computational Sciences at the University ofCantabria.