Iterative methods for ill-posed problems : an introduction / Anatoly B. Bakushinsky, Mikhail Yu. Kokurin, Alexandra Smirnova.

Format:

Book

Author/Creator:

Bakushinskiĭ, A. B. (Anatoliĭ Borisovich)

Contributor:

Kokurin, M. I︠U︡. (Mikhail I︠U︡rʹevich)

Smirnova, A. B. (Aleksandra Borisovna)

Series:

Inverse and ill-posed problems series ; v. 54.

Inverse and ill-posed problems series, 1381-4524 ; 54

Standardized Title:

Iterativnye metody reshenii͡a nekorrektnykh zadach. English

Language:

English

Subjects (All):

Differential equations, Partial--Improperly posed problems.

Differential equations, Partial.

Iterative methods (Mathematics).

Physical Description:

1 online resource (152 p.)

Edition:

1st ed.

Place of Publication:

Berlin ; New York : De Gruyter, c2011.

Language Note:

English

Summary:

Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Contents:

Frontmatter

Preface

Contents

1 The regularity condition. Newton's method

2 The Gauss-Newton method

3 The gradient method

4 Tikhonov's scheme

5 Tikhonov's scheme for linear equations

6 The gradient scheme for linear equations

7 Convergence rates for the approximation methods in the case of linear irregular equations

8 Equations with a convex discrepancy functional by Tikhonov's method

9 Iterative regularization principle

10 The iteratively regularized Gauss-Newton method

11 The stable gradient method for irregular nonlinear equations

12 Relative computational efficiency of iteratively regularized methods

13 Numerical investigation of two-dimensional inverse gravimetry problem

14 Iteratively regularized methods for inverse problem in optical tomography

15 Feigenbaum's universality equation

16 Conclusion

References

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786613166371

9781283166379

1283166372

9783110250657

3110250659

OCLC:

732957489