The application of the method of regularization to integral equations of the first kind of the convolution type

Arsenin, V. Ya.; Савелова, Т.И.

doi:10.1016/0041-5553(69)90137-2

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1975

1979

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Cited by 2 publications

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“…The Arsenin and Ivanov [6] and Arsenin and Savelova [8] papers obtained majorant estimates that relate the decay of the transform of the operator K, the order of the norm £2, and the smoothness of the desired solution. They used complex variable theory to evaluate the error integrals and obtained pointwise estimates.…”

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confidence: 99%

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The effective choice of the smoothing norm in regularization

Cullum¹

1979

Math. Comp.

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Abstract.We consider ill-posed problems of the form(1) g(t) = jQKit, s)fis)ds, 0 < t « 1, where g and K are given, and we must compute /. The Tikhonov regularizaron procedure replaces (1) by a one-parameter family of minimization problems-2 Minimize i\\Kf -g\\ + aft(/))-where ft is a smoothing norm chosen by the user.We demonstrate by example that the choice of ft is not simply a matter of convenience.We then show how this choice affects the convergence rate, and the condition of the problems generated by the regularization. An appropriate choice for ft depends upon the character of the compactness of K and upon the smoothness of the desired solution.

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confidence: 99%

“…Arsenin and Ivanov [6], [7], Arsenin and Savelova [8], Goncharskii, Leonov, and Yagola [9] in more detail in Section 4.…”

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confidence: 99%