Regularization and approximation of linear operator equations in reproducing kernel spaces
Authors:
M. Z. Nashed and Grace Wahba
Journal:
Bull. Amer. Math. Soc. 80 (1974), 12131218
MSC (1970):
Primary 47A50, 65J05, 46G22, 65J05, 41A25; Secondary 65D99, 65F20, 45L10
MathSciNet review:
0365192
Fulltext PDF
References 
Similar Articles 
Additional Information
 1.
N.
Aronszajn, Theory of reproducing
kernels, Trans. Amer. Math. Soc. 68 (1950), 337–404. MR 0051437
(14,479c), http://dx.doi.org/10.1090/S00029947195000514377
 2.
Michael
Golomb and Hans
F. Weinberger, Optimal approximation and error bounds, On
numerical approximation. Proceedings of a Symposium, Madison, April
21–23, 1958, Edited by R. E. Langer. Publication No. 1 of the
Mathematics Research Center, U.S. Army, the University of Wisconsin, The
University of Wisconsin Press, Madison, Wis., 1959, pp. 117–190.
MR
0121970 (22 #12697)
 3.
M.
M. Lavrent′ev, O nekotorykh nekorrektnykh zadachakh
matematicheskoi fiziki, Izdat. Sibirsk. Otdel. Akad. Nauk SSSR,
Novosibirsk, 1962 (Russian). MR 0224319
(36 #7363)
 4.
M.
Z. Nashed, Generalized inverses, normal solvability, and iteration
for singular operator equations, Nonlinear Functional Anal. and Appl.
(Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis.,
1970) Academic Press, New York, 1971, pp. 311–359. MR 0275246
(43 #1003)
 5.
M. Z. Nashed , Some aspects of regularization and approximation of solutions of illposed operator equations, Proc. Army Numerical Analysis Conference, 1972, pp. 163181.
 6.
M.
Z. Nashed and Grace
Wahba, Generalized inverses in reproducing kernel spaces: an
approach to regularization of linear operator equations, SIAM J. Math.
Anal. 5 (1974), 974–987. MR 0358405
(50 #10871)
 7.
M. Z. Nashed and Grace Wahba, Approximate regularized pseudosolutions of linear operator equations when the datavector is not in the range of the operator, (to appear).
 8.
M.
Z. Nashed and Grace
Wahba, Convergence rates of approximate least
squares solutions of linear integral and operator equations of the first
kind, Math. Comp. 28 (1974), 69–80. MR 0461895
(57 #1877), http://dx.doi.org/10.1090/S00255718197404618951
 9.
A.
N. Tihonov, On methods of solving incorrectly formulated
problems, Proc. Internat. Congr. Math. (Moscow, 1966) Izdat.
“Mir”, Moscow, 1968, pp. 720–722 (Russian). MR 0237931
(38 #6208)
 10.
Grace
Wahba, A class of approximate solutions to linear operator
equations, J. Approximation Theory 9 (1973),
61–77. MR
0386284 (52 #7142)
 1.
 N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337404. MR 14, 479. MR 51437
 2.
 M. Golomb and H. F. Weinberger, Optimal approximation and error bounds, On Numerical Approximation (R. E. Langer, editor), Univ. of Wisconsin Press, Madison, Wis., 1959, pp. 117190. MR 121970
 3.
 M. M. Lavrent ev, Some improperly posed problems of mathematical physics, Izdat. Sibirsk. Otdel. Akad. Nauk SSSR. Novosibirsk, 1962; English transl., Springer Tracts in Natural Philosophy, vol. 11, SpringerVerlag, Berlin, 1967. MR 36 #5487; #7363. MR 224319
 4.
 M. Z. Nashed, Generalized inverses, normal solvability, and iteration for singular operator equations, Nonlinear Functional Analysis and Applications (Proc. Advanced Sem. Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970), Academic Press, New York, 1971, pp. 311359. MR 43 #1003. MR 275246
 5.
 M. Z. Nashed , Some aspects of regularization and approximation of solutions of illposed operator equations, Proc. Army Numerical Analysis Conference, 1972, pp. 163181.
 6.
 M. Z. Nashed and Grace Wahba, Generalized inverses in reproducing kernel spaces: An approach to regularization of linear operator equations, SIAM J. Math. Anal. (to appear). MR 358405
 7.
 M. Z. Nashed and Grace Wahba, Approximate regularized pseudosolutions of linear operator equations when the datavector is not in the range of the operator, (to appear).
 8.
 M. Z. Nashed and Grace Wahba, Rates of convergence and approximate least squares solutions of linear integral and operator equations, Math. Comp. 28 (1974), 6980. MR 461895
 9.
 A. N. Tihonov, On methods of solving incorrect problems, Proc. Internat. Congress Math. (Moscow, 1966), "Mir", Moscow, 1968, pp. 720722; English transl., Amer. Math. Soc. Transl. (2) 70 (1968), 222224. MR 38 #6208. MR 237931
 10.
 Grace Wahba, A class of approximate solutions to linear operator equations, J. Approximation Theory 9 (1973), 6177. MR 386284
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Additional Information
DOI:
http://dx.doi.org/10.1090/S000299041974136840
PII:
S 00029904(1974)136840
