A Contemporary Study of Iterative Method

DescriptionA Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand.Key FeaturesContains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spacesEncompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiographyExplores the uses of computation of iterative methods across non-linear analysisUniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between optionsReadershipGraduate students and some (appropriately skilled) senior undergraduate students, researchers and practitioners in applied and computational mathematics, optimization and related sciences requiring the solution to nonlinear equations situated in a scalar and an abstract domainTable of ContentsThe majorization method in the Kantorovich theoryDirectional Newton methodsNewton’s methodGeneralized equationsGauss–Newton methodGauss–Newton method for convex optimizationProximal Gauss–Newton methodMultistep modified Newton–Hermitian and Skew-Hermitian Splitting methodSecant-like methods in chemistryRobust convergence of Newton’s method for cone inclusion problemGauss–Newton method for convex composite optimizationDomain of parametersNewton’s method for solving optimal shape design problemsOsada methodNewton’s method to solve equations with solutions of multiplicity greater than oneLaguerre-like method for multiple zerosTraub’s method for multiple rootsShadowing lemma for operators with chaotic behaviorInexact two-point Newton-like methodsTwo-step Newton methodsIntroduction to complex dynamicsConvergence and the dynamics of Chebyshev–Halley type methodsConvergence planes of iterative methodsConvergence and dynamics of a higher order family of iterative methodsConvergence and dynamics of iterative methods for multiple zerosAuthor DescriptionProfessor Alberto Magreñán (Department of Mathematics, Universidad Internacional de La Rioja, Spain). Magreñán has published 43 documents. He works in operator theory, computational mathematics, Iterative methods, dynamical study and computation.– Department of Mathematics, Universidad Internacional de La Rioja, La Rioja, SpainProfessor Ioannis Argyros (Department of Mathematical Sciences Cameron University, Lawton, OK, USA) has published 329 indexed documents and 25 books. Argyros is interested in theories of inequalities, operators, computational mathematics and iterative methods, and banach spaces.– Department of Mathematical Sciences, Cameron University, Lawton, OK, USA