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Demonstrates the application of DSM to solve a broad range of operator equations
The dynamical systems method (DSM) is a powerful computational method for solving operator equations. With this book as their guide, readers will master the application of DSM to solve a variety of linear and nonlinear problems as well as ill-posed and well-posed problems. The authors offer a clear, step-by-step, systematic development of DSM that enables readers to grasp the method's underlying logic and its numerous applications.
Dynamical Systems Method and Applications begins with a general introduction and then sets forth the scope of DSM in Part One. Part Two introduces the discrepancy principle, and Part Three offers examples of numerical applications of DSM to solve a broad range of problems in science and engineering.
Written by internationally recognized authorities on the topic, Dynamical Systems Method and Applications is an excellent book for courses on numerical analysis, dynamical systems, operator theory, and applied mathematics at the graduate level. The book also serves as a valuable resource for professionals in the fields of mathematics, physics, and engineering.
Ill-posed problems
DSM for well-posed problems
DSM and linear ill-posed problems
Some inequalities
DSM for monotone operators
DSM for general nonlinear operator equations
DSM for operators satisfying a spectral assumption
DSM in Banach spaces
DSM and Newton-type methods without inversion of the derivative
DSM and unbounded operators
DSM and nonsmooth operators
DSM as a theoretical tool
DSM and iterative methods
Numerical problems arising in applications
Solving linear operator equations by a Newton-type DSM
DSM of gradient type for solving linear operator equations
DSM for solving linear equations with finite-rank operators
A discrepancy principle for equations with monotone continuous operators
DSM of Newton-type for solving operator equations with minimal smoothness assumptions
DSM of gradient type
DSM of simple iteration type
DSM for solving nonlinear operator equations in Banach spaces
Solving linear operator equations by the DSM
Stable solutions of Hammerstein-type integral equations
Inversion of the Laplace transform from the real axis using an adaptive iterative method