Parimah Kazemi, Robert J. Renka
Abstract:
Given an ill-posed linear operator equation Au=f in a Hilbert
space, we formulate a variational problem using Tikhonov regularization
with a Sobolev norm of u, and we treat the variational problem by a
Sobolev gradient flow.
We show that the gradient system has a unique global solution for which
the asymptotic limit exists with convergence in the strong sense using
the Sobolev norm, and that the variational problem therefore has a unique
global solution.
We present results of numerical experiments that demonstrates the benefits
of using a Sobolev norm for the regularizing term.
Published February 10, 2014.
Math Subject Classifications: 47A52, 65D25, 65F22.
Key Words: Gradient system; Ill-posed problem; least squares;
Sobolev gradient; Tikhonov regularization.
Show me the PDF(212 K), TEX and other files for this article.
Parimah Kazemi Department of Mathematics and Computer Science Ripon College, P. O. Box 248 Ripon, WI 54971-0248, USA email: parimah.kazemi@gmail.com | |
Robert J. Renka Department of Computer Science & Engineering University of North Texas Denton, TX 76203-1366, USA email: robert.renka@unt.edu |
Return to the table of contents
for this conference.
Return to the EJDE web page