Dynamical Systems Method and Applications (PDF)

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. Additional featured
topics 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 figures
and tables to help readers grasp and apply new concepts. Numerical
examples offer original theoretical results based on the solution
of practical problems involving ill-conditioned linear algebraic
systems, and stable differentiation of noisy data.

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.