Parimah Kazemi, Robert J. Renka
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.
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| Parimah Kazemi |
Department of Mathematics and Computer Science
Ripon College, P. O. Box 248
Ripon, WI 54971-0248, USA
| Robert J. Renka |
Department of Computer Science & Engineering
University of North Texas
Denton, TX 76203-1366, USA
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