IJPAM: Volume 58, No. 4 (2010)

NAIVE VS. REGULARIZED.
NUMERICAL STUDY

Alexandra Smirnova$^1$, MaryGeorge L. Whitney$^2$
$^{1,2}$Department of Mathematics and Statistics
Georgia State University
Atlanta, GA 30303, USA
e-mail: [email protected]
e-mail: [email protected]


Abstract.In computational mathematics and applications, there are numerous examples of problems that are unstable with respect to noise in the input data. Classical numerical algorithms, when used for such problems, turn out to be divergent. Hence, in order to solve the problem in a stable fashion, one has to combine a numerical method with special regularization techniques that would take advantage of an a priori information available in each particular case. In this paper, numerical analysis of Tikhonov's (variational) regularization for a first kind integral equation is given. The regularization parameter is computed by the discrepancy principle of Morozov.

Received: January 15, 2010

AMS Subject Classification: 47A52, 65F22

Key Words and Phrases: Tikhonov regularization, Morozov discrepancy principle, ill-posed problems, integral equations

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 4