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.
