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Nashed, M. Z.; Wahba, Grace

Regularization and approximation of linear operator equations in reproducing kernel spaces. (English) Zbl 0309.47012

Bull. Am. Math. Soc. 80, 1213-1218 (1974).
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Cited in 7 Documents

MSC:

47A50 Equations and inequalities involving linear operators, with vector unknowns
65R20 Numerical methods for integral equations
65F20 Numerical solutions to overdetermined systems, pseudoinverses
65D99 Numerical approximation and computational geometry (primarily algorithms)
65J05 General theory of numerical analysis in abstract spaces
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References:

[1] N. Aronszajn, Theory of reproducing kernels, Trans. Amer. Math. Soc. 68 (1950), 337 – 404. · Zbl 0037.20701
[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. · Zbl 0092.05802
[3] О некоторых некорректных задачах математической физики, Издат. Сибирск. Отдел. Акад. Наук СССР, Новосибирск, 1962 (Руссиан).
[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.
[5] M. Z. Nashed , Some aspects of regularization and approximation of solutions of illposed operator equations, Proc. Army Numerical Analysis Conference, 1972, pp. 163-181.
[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. · Zbl 0287.47009 · doi:10.1137/0505095
[7] M. Z. Nashed and Grace Wahba, Approximate regularized pseudosolutions of linear operator equations when the data-vector is not in the range of the operator, (to appear). · Zbl 0273.45012
[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. · Zbl 0273.45012
[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).
[10] Grace Wahba, A class of approximate solutions to linear operator equations, J. Approximation Theory 9 (1973), 61 – 77. · Zbl 0267.45015
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