
Polynomial Operator Equations in Abstract Spaces and Applications
in Abstract Spaces and Applications
Ioannis K. Argyros(Author)
CRC Press
1st Edition
Published on 25. March 1998
Book
Hardback
VIII, 573 pages
978-0-8493-8702-9 (ISBN)
Description
Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques.
Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings.
Topics include:
Special cases of nonlinear operator equations
Solution of polynomial operator equations of positive integer degree n
Results on global existence theorems not related with contractions
Galois theory
Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas
Results on the various Chandrasekhar equations
Weierstrass theorem
Matrix representations
Lagrange and Hermite interpolation
Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space
The materials discussed can be used for the following studies
Advanced numerical analysis
Numerical functional analysis
Functional analysis
Approximation theory
Integral and differential equations
Tables include
Numerical solutions for Chandrasekhar's equation I to VI
Error bounds comparison
Accelerations schemes I and II for Newton's method
Newton's method
Secant method
The self-contained text thoroughly details results, adds exercises for each chapter, and includes several applications for the solution of integral and differential equations throughout every chapter.
Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings.
Topics include:
Special cases of nonlinear operator equations
Solution of polynomial operator equations of positive integer degree n
Results on global existence theorems not related with contractions
Galois theory
Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas
Results on the various Chandrasekhar equations
Weierstrass theorem
Matrix representations
Lagrange and Hermite interpolation
Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space
The materials discussed can be used for the following studies
Advanced numerical analysis
Numerical functional analysis
Functional analysis
Approximation theory
Integral and differential equations
Tables include
Numerical solutions for Chandrasekhar's equation I to VI
Error bounds comparison
Accelerations schemes I and II for Newton's method
Newton's method
Secant method
The self-contained text thoroughly details results, adds exercises for each chapter, and includes several applications for the solution of integral and differential equations throughout every chapter.
Reviews / Votes
"This book provides a valuable service to those mathematicians working in the area of polynomial operator equations...The theoretical material addressed has a spectrum of applications...applications [that are] quite relevant and important...Anyone doing research in this area should have a copy of this monograph."Patrick J. Van Fleet, Mathematical and Information Sciences, Huntsville, Texas
"A comprehensive presentation of this rapidly growing field...benefiting not only those working in the field but also those interested in, and in need of, information about specific results or techniques...Clear...Logical...Elegant...The author has achieved the optimum at this point."
- Dr. George Anastassiou, University of Memphis, Tennessee
More details
Language
English
Place of publication
Bosa Roca
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional and scholarly
Professional Practice & Development
Illustrations
10 s/w Tabellen
10 Tables, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 36 mm
Weight
1039 gr
ISBN-13
978-0-8493-8702-9 (9780849387029)
Schweitzer Classification
Other editions
Additional editions

Ioannis K. Argyros
Polynomial Operator Equations in Abstract Spaces and Applications
E-Book
10/2020
1st Edition
CRC Press
€87.49
Available for download

Ioannis K. Argyros
Polynomial Operator Equations in Abstract Spaces and Applications
E-Book
10/2020
1st Edition
CRC Press
€87.49
Available for download

Ioannis K. Argyros
Polynomial Operator Equations in Abstract Spaces and Applications
in Abstract Spaces and Applications
Book
06/2020
1st Edition
CRC Press
€76.87
Shipment within 15-20 days
Person
Argyros\, Ioannis K.
Content
Introduction 1. Quadratic Equations and Perturbation Theory 2. More Methods for Solving Quadratic Equations 3. Polynomial Equations in Banach Space 4. Integral and Differential Equations 5. Polynomial Operators in Linear Spaces 6. General Methods for Solving Nonlinear Equations