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Numerical methods for ill-posed, linear problems

Citation

Stevens, Thomas (1975) Numerical methods for ill-posed, linear problems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:03292013-151040800

Abstract

A means of assessing the effectiveness of methods used in the numerical solution of various linear ill-posed problems is outlined. Two methods: Tikhonov' s method of regularization and the quasireversibility method of Lattès and Lions are appraised from this point of view.

In the former method, Tikhonov provides a useful means for incorporating a constraint into numerical algorithms. The analysis suggests that the approach can be generalized to embody constraints other than those employed by Tikhonov. This is effected and the general "T-method" is the result.

A T-method is used on an extended version of the backwards heat equation with spatially variable coefficients. Numerical computations based upon it are performed.

The statistical method developed by Franklin is shown to have an interpretation as a T-method. This interpretation, although somewhat loose, does explain some empirical convergence properties which are difficult to pin down via a purely statistical argument.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Ill-posed, Numerical, Hilbert Space
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Franklin, Joel N.
Thesis Committee:
  • Franklin, Joel N. (chair)
  • Whitham, Gerald Beresford
  • Luxemburg, W. A. J.
  • Cohen, Donald S.
Defense Date:9 August 1974
Non-Caltech Author Email:tom.stevens (AT) opg.com
Record Number:CaltechTHESIS:03292013-151040800
Persistent URL:http://resolver.caltech.edu/CaltechTHESIS:03292013-151040800
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7567
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:29 Mar 2013 22:28
Last Modified:11 Feb 2014 00:07

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