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The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications..
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This digital document is an article from Photo Marketing, published by Photo Marketing Association International on January 1, 2003. The length of the article is 1585 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Troubleshooting digital camera card problems: a digital camera card that is damaged or formatted improperly can mean headaches for consumers and retail labs. Here, three retailers share their methods of dealing with problem cards. (Retailing).
Author: Jennifer Barr Kruger
Publication:Photo Marketing (Magazine/Journal)
Date: January 1, 2003
Publisher: Photo Marketing Association International
Volume: 78 Issue: 1 Page: 27(2)

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Price: $5.95 [Notify me when price goes down.]

This digital document is an article from Church & State, published by Americans United for Separation of Church and State on May 1, 2002. The length of the article is 496 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Calif. school district accused of improperly teaching about Islam. (People & Events).(California)(Brief Article)
Publication:Church & State (Refereed)
Date: May 1, 2002
Publisher: Americans United for Separation of Church and State
Volume: 55 Issue: 5 Page: 19(2)

Article Type: Brief Article

Distributed by Thomson Gale.
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Uses a strong computational and truly interdisciplinary treatment to introduce applied inverse theory. The author created the Mollification Method as a means of dealing with ill-posed problems. Although the presentation focuses on problems with origins in mechanical engineering, many of the ideas and techniques can be easily applied to a broad range of situations..
Price: $120.00 [Notify me when price goes down.]