Buch, Englisch, 586 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1039 g
Buch, Englisch, 586 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1039 g
ISBN: 978-0-8493-8702-9
Verlag: CRC Press
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.
Zielgruppe
Professional Practice & Development
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
Weitere Infos & Material
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
