Polynomial Operator Equations in Abstract Spaces and Applications

Ioannis K. Argyros

ISBN 10: 0849387027 / ISBN 13: 9780849387029

Editore: CRC Press, 1998

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nach der Bestellung gedruckt Neuware - Printed after ordering - 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 equationsSolution of polynomial operator equations of positive integer degree nResults on global existence theorems not related with contractionsGalois theoryPolynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areasResults on the various Chandrasekhar equationsWeierstrass theoremMatrix representationsLagrange and Hermite interpolationBounds of polynomial equations in Banach space, Banach algebra, and Hilbert spaceThe materials discussed can be used for the following studiesAdvanced numerical analysisNumerical functional analysisFunctional analysisApproximation theoryIntegral and differential equationsTables includeNumerical solutions for Chandrasekhar's equation I to VIError bounds comparisonAccelerations schemes I and II for Newton's methodNewton's methodSecant methodThe 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.

Codice articolo 9780849387029

Dati bibliografici

• Titolo: Polynomial Operator Equations in Abstract Spaces and Applications
• Editore: CRC Press
• Data di pubblicazione: 1998
• Lingua: Inglese
• ISBN 10: 0849387027
• ISBN 13: 9780849387029
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 240 L x 161 A x 36 P (millimetri) 240 millimetri di larghezza per 161 millimetri di altezza per 36 millimetri di profondità
• Peso: 1039 grammi

Descrizione articolo

Riassunto

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.

Informazioni sull?autore

Argyros\, Ioannis K.