Control Perspectives on Numerical Algorithms and Matrix Problems organizes the analysis and design of iterative numerical methods from a control perspective. The authors discuss a variety of applications, including iterative methods for linear and nonlinear systems of equations, neural networks for linear and quadratic programming problems, support vector machines, integration and shooting methods for ordinary differential equations, matrix preconditioning, matrix stability, and polynomial zero finding. This book opens up a new field of interdisciplinary research that should lead to insights in the areas of both control and numerical analysis and shows that a wide range of applications can be approached from—and benefit from—a control perspective. Audience Control Perspectives on Numerical Algorithms and Matrix Problems is intended for researchers in applied mathematics and control as well as senior undergraduate and graduate students in both of these fields. Engineers and scientists who design algorithms on a heuristic basis and are looking for a framework may also be interested in the book. Contents List of Figures; List of Tables; Preface; Chapter 1: Brief Review of Control and Stability Theory; Chapter 2: Algorithms as Dynamical Systems with Feedback; Chapter 3: Optimal Control and Variable Structure Design of Iterative Methods; Chapter 4: Neural-Gradient Dynamical Systems for Linear and Quadratic Programming Problems; Chapter 5: Control Tools in the Numerical Solution of Ordinary Differential Equations and in Matrix Problems; Chapter 6: Epilogue; Bibliography; Index.
Science-Math, Mathematics, Pure-Mathematics, Calculus,