Titlebook: Regularization of Ill-Posed Problems by Iteration Methods; S. F. Gilyazov,N. L. Gol’dman Book 2000 Springer Science+Business Media B.V. 20

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Regularizing Algorithms for Linear Ill-Posed Problems: Unified Approach,Let .: . be a linear bounded operator between Hubert spaces . and .. For any element . ? . we shall consider the set . In a general case the set .. can be empty.

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Iteration Steepest Descent Methods for Linear Operator Equations,Our investigation of regularizing properties of iterative methods for the stable solution of ill-posed problems starts with analysis of steepest descent methods.

芳香一點

Iteration Conjugate Direction Methods for Linear Operator Equations,Iterative methods of steepest descent considered in Chapter 2 provide the best rate of convergence in each iteration of the process. However such a ‘local optimal strategy’ is not so suitable for solving the problem (1.1.1), (1.1.6) of computation of a global minimum of a quadratic functional.

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Iteration Steepest Descent Methods for Nonlinear Operator Equations,In this chapter we investigate regularizing iteration methods for approximate solution of the nonlinear operator equation . where .: . → . is a nonlinear operator, . and . are the Hilbert spaces, . ?. is the given element. We assume that the equation (4.1.1) has the unique solution ..? ..

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Iteration Methods for Ill-Posed Constrained Minimization Problems,Let us consider the problem of an approximate solution of a nonlinear operator equation of the first kind . where . (.): . → . is defined on the nonempty set . (.) ? . and . are Hubert spaces.

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Introduction,ot exist, and even if they exist they need not be unique and stable, i.e., continuously depending on the input data. To obtain stable numerical solutions of problems for which the Hadamard conditions of correctness [83, 84] are not satisfied, the regularization methods must be applied.

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Descriptive Regularization Algorithms on the basis of the Conjugate Gradient Projection method,aditional way to regularize them, i.e., to convert them into related well-posed problems, is applied. This way is based on utilization of quantitative information about the level of errors in the input data and on greatly general . information pertaining to smoothness of the solution. This ensures a