Methods for solving operator equations

著者

• Tanana, Vitaliĭ Pavlovich

書誌事項

Methods for solving operator equations

V. P. Tanana

（Inverse and ill-posed problems series）

VSP, 1997

注記

Includes bibliographical references (p. 209-223)

内容説明・目次

内容説明

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information.

目次

• 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.

「Nielsen BookData」 より

詳細情報

• NII書誌ID(NCID): BA47951633
• ISBN:
  • 9067642371
• 出版国コード: ne
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Utrecht, The Netherlands
• ページ数/冊数: 223 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA2420606X