Academic Press A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications

Product Description A 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. Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography Explores the uses of computation of iterative methods across non-linear analysis Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options Review "“Contemporary in the title means that the coverage is state-of-the-art, with all currently-useful methods being shown. The level of detail is reasonable for an encyclopedia, and each chapter is extensively footnoted with references to research papers. Usually each chapter describes the method, quotes some theorems about the conditions under which it will succeed (occasionally with proofs), and usually a contrived numeric example to show how it works. There’s usually some discussion of convergence speed." --MAA Reviews Review Evaluates and compares advances in iterative techniques, discussing their numerous applications in mathematics, engineering, economics, biology and other applied sciences About the Author Professor 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. Professor 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.