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A Modified Tikhonov Regularization Method for Solving Ill-posed Problems ——(1)Constroution of Regularization

Jia Wang

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Abstract

In this paper, a new class of improved regularization methods, called modified Tikhonov regularization (MTR) for solving ill_posed problems of the first kind of operator equation with noisy data is constructed. By a priori choosing regularization parameter, optimal convergence order of the regularized solution is obtained. As compared with ordinary Tikhonov regularization (OTR), this new scheme can achieve higher optimum asymptotic order of the regularized solution by selecting an auxiliary parameter.

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What this paper is about

In this paper, a new class of improved regularization methods, called modified Tikhonov regularization (MTR) for solving ill_posed problems of the first kind of operator equation with noisy data is constructed. By a priori choosing regularization parameter, optimal convergence order of the regularized solution is obtained. As compared with ordinary Tikhonov regularization (OTR), this new scheme can achieve higher optimum asymptotic order of the regularized solution by selecting an auxiliary parameter.

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Available abstract

In this paper, a new class of improved regularization methods, called modified Tikhonov regularization (MTR) for solving ill_posed problems of the first kind of operator equation with noisy data is constructed. By a priori choosing regularization parameter, optimal convergence order of the regularized solution is obtained. As compared with ordinary Tikhonov regularization (OTR), this new scheme can achieve higher optimum asymptotic order of the regularized solution by selecting an auxiliary parameter.

Key concepts: Tikhonov regularization, Backus–Gilbert method, Regularization perspectives on support vector machines, Regularization (linguistics), Mathematics, A priori and a posteriori, Proximal gradient methods for learning, Applied mathematics

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