Conjugate gradient type methods for ill-posed problems
著者
書誌事項
Conjugate gradient type methods for ill-posed problems
（Pitman research notes in mathematics series, 327）
Longman Scientific & Technical , Wiley, 1995
大学図書館所蔵 件 / 全48件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and index
内容説明・目次
内容説明
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more
This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations.
The main tool for the analysis is the connection of conjugate gradient
type methods to real orthogonal polynomials, and elementary
properties of these polynomials. These prerequisites are provided in
a first chapter. Applications to image reconstruction and inverse
heat transfer problems are pointed out, and exemplarily numerical
results are shown for these applications.
目次
1. Conjugate Gradient Type Methods 2. Regularizing Properties of MR and CGNE 3. Regularizing Properties of CG and CGME 4. On the Number of Iterations 5. A Minimal Residual Method for Indefinite Problems
「Nielsen BookData」 より