Abstract
In this chapter, we investigate the conjugate gradient method for solving first-kind integral equations in two variables. A typical application problem would be the 2-D image reconstruction problem. For example, if we take a picture from far above the atmosphere, owing to the precision of the physical equipment, there will be some deviation between the picture and the original object, not to mention the effects posed by air turbulence, clouds, and perhaps pollution.
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References
C.W. Groetsch, The theory of Tikhonov regularization for Fredholm equations of the first kind, Pitman Advanced Publishing Program 105, London, 1995.
G.H. Golub and C. Van Loan, Matrix computations, 3rd ed., Johns Hopkins, Baltimore, 1996.
M. Hanke, Conjugate gradient type methods for ill-posed problems, Pitman Res. Notes Math. Ser. 327, Longman/Wiley, Harlow-New York, 1995.
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Cheng, H., Bertram, B. (2002). On the Stopping Criteria for Conjugate Gradient Solutions of First-Kind Integral Equations in Two Variables. In: Constanda, C., Schiavone, P., Mioduchowski, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0111-3_9
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DOI: https://doi.org/10.1007/978-1-4612-0111-3_9
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6617-4
Online ISBN: 978-1-4612-0111-3
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