Numerical approximation of minimum norm solutions of for special
Author:
Glenn R. Luecke
Journal:
Math. Comp. 53 (1989), 563569
MSC:
Primary 65R20; Secondary 47A50, 65J10
MathSciNet review:
983562
Fulltext PDF Free Access
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Abstract: Let be continuous and linear and assume . Define by . Assume K has the property that (a) for all and (b) if a.e., then for all . For example, if , is Lebesgue measure and if satisfies a Lipschitz condition in x, then K has the above property. Assume K satisfies this property and is a minimum norm solution of the firstkind integral equation for all . It is shown that is the norm limit of linear combinations of the 's. It is then shown how to choose constants to minimize without knowing what is. This paper also contains results on how to choose the 's as well as numerical examples illustrating the theory.
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 R. S. Anderssen & P. M. Prenter, "A formal comparison of methods proposed for the numerical solution of first kind integral equations," J. Austral. Math. Soc. Ser. B, v. 22, 1981, pp. 488500. MR 626939 (82h:65094)
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 Glenn R. Luecke & Kevin R. Hickey, "A note on the filtered least squares minimal norm solution of first kind equations," J. Math. Anal. Appl., v. 100, no. 2, 1984, pp. 635641. MR 743345 (85k:45022)
 [4]
 Glenn R. Luecke & Kevin R. Hickey, "Convergence of approximate solutions of operator equations," Houston J. Math., v. 11, no. 3, 1985, pp. 345353. MR 808651 (87a:47019)
 [5]
 Manfred R. Trummer, "A method for solving illposed linear operator equations," SIAM J. Numer. Anal., v. 21, no. 4, 1984, pp. 729737. MR 749367 (85m:65051)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198909835629
PII:
S 00255718(1989)09835629
Keywords:
Firstkind integral equation,
numerical solution of firstkind integral equations
Article copyright:
© Copyright 1989 American Mathematical Society
