Iterative Methods for Nonlinear ILL-posed Problems: Numerical Functional Analysis - Softcover

Elmahdy, Atef Ibrahim; George, Santhosh

Softcover

ISBN 10: 3848482622 ISBN 13: 9783848482627

Publisher: LAP LAMBERT Academic Publishing, 2012

Synopsis

Many problems in science and engineering have their mathematical formulation as an operator equation of the form F(x) = y, where F is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not be often possible or may not be worth looking for due to physical constraints. In such situation, it is desirable to know how the so-called approximate solution approximates the exact solution, and what would be the error involved in such procedures. The main focus of the book is on the study of stably solving nonlinear ill posed operator equations of the form F(x)=y, with monotone nonlinear operator F in an infinite dimensional real Hilbert space X, that is , F obeys the monotonicity property. It is assumed that the exact data y is unknown and usually only noisy data are available. Problems of this type arise in a number of applications. Since the solution does not depend continuously on the data, the ill-posed problem has to be regularized. We considered iterative methods which converge to the unique solution of the method of Lavrentiev regularization.

About this title

About the Author

Dr. Atef Elmahdy obtained his PhD degree in the Mathematical and Computational Sciences in the field of Ill-Posed Problems. He is the author of several articles published in refereed journals and a reviewer in some international journals. He has worked as an assistant lect. and now, as a lecturer of Pure Math. at Mansoura University, Egypt.

Edition details

• Publisher: LAP LAMBERT Academic Publishing
• Publication date: 2012
• ISBN 10: 3848482622
• ISBN 13: 9783848482627
• Binding: Paperback
• Language: English
• Number of pages: 100