1974
DOI: 10.1016/0041-5553(74)90052-4
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The application of a class of regularizing algorithms to the solution of integral equations of the first kind of the convolution type in banach space

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1986
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(3 citation statements)
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“…One obtains order-exact estimates of the error of the method, under an infinitely small variance of the noise 02 , and the quasioptimal regularizer of this class [28] with the corresponding rules for the selection of the values of ~; similar investigations have been carried out also in the case of errors in the operator [155,252,302]. One has investigated [33] a method of summation of Fourier series, close to the optimal one, consisting in the rejection not only of the infinite part of the series but also of the terms with strongly noise-perturbed coefficients.…”
Section: Methodsmentioning
confidence: 96%
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“…One obtains order-exact estimates of the error of the method, under an infinitely small variance of the noise 02 , and the quasioptimal regularizer of this class [28] with the corresponding rules for the selection of the values of ~; similar investigations have been carried out also in the case of errors in the operator [155,252,302]. One has investigated [33] a method of summation of Fourier series, close to the optimal one, consisting in the rejection not only of the infinite part of the series but also of the terms with strongly noise-perturbed coefficients.…”
Section: Methodsmentioning
confidence: 96%
“…A general scheme of a projection method for a linear injection A, in the form of the replacement of the equation (i) by the equations q~Ap~x = q~y, 0 < x & ~, where p~:X + X and q~:Y + Y are bounded linear operators and X, Y are Banach spaces, has been considered in [302]. For the applicability of the method in the case of a perturbed right-hand side it is necessary and sufficient that~ II(q~Ap~)-~}16 ~ 0~ ~) r+0, and that the exact solution should belong to the approximated set {x:~q~Ap~)-~q~Ax + x, 9 § 0}.…”
Section: Projection Methodsmentioning
confidence: 99%
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