Methods for Solving Operator Equations
VSP International Science Publishers (Verlag)
978-90-6764-237-8 (ISBN)
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Part 1 Regularization of linear operator equations: classification of ill-posed problems and the concept of the optimal method; the estimate from below for Dopt; the error of the regularization method; the algorithmic peculiarities of the generalized residual principle; the error of the quasi-solutions method; the regularization method with the parameter a chosen by the residual; the projection regularization method; on the choice of the optimal regularization parameter; optimal methods for solving unstable problems with additional information on the operator A; on the regularization of operator equations of the first kind with the approximately given operator and on the choice of the regularization parameter; the generalized reesidual principle; the optimum of the generalized residual principle. Part 2 Finite-dimensional methods of constructing regularized solutions: the notion of t-uniform convergence of linear operators; the general scheme of finite-dimensional approximation in the regularization method; application of the general scheme to the projection and finite difference methods; the general scheme of finite-dimensional approximation in the generalized residual method; the iterative method for determining the finite-dimensional approximation in the generalized residual principle; the general scheme of finite-dimensional approximations in the quasi-solution method; the necessary and sufficient conditions for the convergence of finite-imenaional approximations in the regularized method; on the discretization of the variational problems (1.11.5); finite-dimensional approximation of regularized solutions; application. Part 3 Regulariztion of non-linear operator equations: approximate solution of non-linear operator equations with a disturbed operator by the regularization method; approximate solution of implicit operator equations of the first kind by the regularization method; optimal by the order method for solving non-linear unstable problems.
| Erscheint lt. Verlag | 1.3.1997 |
|---|---|
| Reihe/Serie | Inverse and Ill-Posed Problems Series ; 8 |
| Verlagsort | Zeist |
| Sprache | englisch |
| Gewicht | 500 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| ISBN-10 | 90-6764-237-1 / 9067642371 |
| ISBN-13 | 978-90-6764-237-8 / 9789067642378 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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