Methods and Applications : Theoretical Developments and Numerical ExampleseBook - 2012
The dynamical systems method (DSM) is a powerful computationalmethod for solving operator equations. With this book as theirguide, readers will master the application of DSM to solve avariety of linear and nonlinear problems as well as ill-posed andwell-posed problems. The authors offer a clear, step-by-step,systematic development of DSM that enables readers to grasp themethod's underlying logic and its numerous applications.
Dynamical Systems Method and Applications begins with ageneral introduction and then sets forth the scope of DSM in PartOne. Part Two introduces the discrepancy principle, and Part Threeoffers examples of numerical applications of DSM to solve a broadrange of problems in science and engineering. Additional featuredtopics include:
General nonlinear operator equations
Operators satisfying a spectral assumption
Newton-type methods without inversion of the derivative
Numerical problems arising in applications
Stable numerical differentiation
Stable solution to ill-conditioned linear algebraic systems
Throughout the chapters, the authors employ the use of figuresand tables to help readers grasp and apply new concepts. Numericalexamples offer original theoretical results based on the solutionof practical problems involving ill-conditioned linear algebraicsystems, and stable differentiation of noisy data.
Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellentbook for courses on numerical analysis, dynamical systems, operatortheory, and applied mathematics at the graduate level. The bookalso serves as a valuable resource for professionals in the fieldsof mathematics, physics, and engineering.