Newton-like methods and polynomiographic visualization of modified Thakur processes
Gabriela Ioana Usurelu, Andreea Bejenaru, Mihai Postolache
Abstract
The content of this paper is twofold. First, it aims to provide some new Newton-like methods for solving the root-finding problem in the complex plane. Moreover a convergence test for the resulted methods is phrased and proved. The pseudo-Newton method of Kalantari for finding the maximum modulus of complex polynomials arises as particular case of the newly proposed procedures. Secondly, a recently introduced Thakur iterative process is used in connection with the newly described methods. Its stability and data dependence is subject to analysis. Ultimately, an illustrative analysis regarding some modified Thakur iteration procedures, is obtained via polynomiographic techniques.
Topics & Concepts
MathematicsNewton's methodConvergence (economics)Applied mathematicsStability (learning theory)Iterative methodAlgorithmComputer scienceNonlinear systemMachine learningEconomic growthPhysicsEconomicsQuantum mechanicsIterative Methods for Nonlinear EquationsAdvanced Optimization Algorithms ResearchOptimization and Variational Analysis