The Choice Of Regulariztion Parameters On Model Function Mehtod

In fact, the electiveness and success of a regularization method depends strongly onthe choice of the regularization parameter. Regularization parameter is generallyexperience or priori in many inverse problems of mathematical physics. Therefore it isunsatisfying from both the practical and the conceptual points of view. On the otherhand,to obtain a feasible regularization parameter will be cost a large amount of time. Thechoice of the regularization parameter is a key matter for ensuring proper regularization.This dissertation mainly studies the method for determining the regularizationparameters and its applications. First, we study the model function method for choosingregularization parameter on condition that perturbed operator and noisy data for solvingoperator equations of the first kind. Secondly, we integrate the spirit of model functionmethod into L-curve. The dissertation is organized as follows:In the first chapter, Some introduction of this paper is described, including theobjectives and content of this paper, the significance and development, the routes andmethods, etc.In the second chapter, it is a survey of related theory of the choice on regularizationparameter and model function method. Including basic conception of regularizationparameter, some frequent choice strategy of regularization parameter, model functionmethod and some frequent model function.In the third chapter, traditional methods are only on condition that noisy data to studythe choice of regularization parameter. we study the model function method for choosingregularization parameter on condition that perturbed operator and noisy data for solvingoperator equations of the first kind. Numerical experiments for integral equations of t hefirst kind are presented to illust rate the efficiency of the proposed algorithms.In the fourth chapter, L-curve is a good method in some frequent choice strategy ofregularization parameter because of its error estimate of unknown in advance andminimum value in place. We integrate the spirit of model function method into L-curve.At last, the full work of the paper is summarized, and looking for the next study.