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2011•Journal of applied mathematics & informaticsRequires access

REGULARIZED SOLUTION TO THE FREDHOLM INTEGRAL EQUATION OF THE FIRST KIND WITH NOISY DATA y

Jin Wen, Ting Wei

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Abstract

In this paper, we use a modifled Tikhonov regularization method to solve the Fredholm integral equation of the flrst kind. Under the as- sumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of mea- sured points. Some numerical experiments show that the proposed method is efiective and stable.

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What this paper is about

In this paper, we use a modifled Tikhonov regularization method to solve the Fredholm integral equation of the flrst kind. Under the as- sumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of mea- sured points. Some numerical experiments show that the proposed method is efiective and stable.

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Available abstract

In this paper, we use a modifled Tikhonov regularization method to solve the Fredholm integral equation of the flrst kind. Under the as- sumption that measured data are contaminated with deterministic errors, we give two error estimates. The convergence rates can be obtained under the suitable choices of regularization parameters and the number of mea- sured points. Some numerical experiments show that the proposed method is efiective and stable.

Key concepts: Tikhonov regularization, Fredholm integral equation, Mathematics, Regularization (linguistics), Integral equation, Noisy data, Convergence (economics), Applied mathematics

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