1.

Record Nr.

UNINA9910962247203321

Autore

Bakushinskiĭ A. B (Anatoliĭ Borisovich)

Titolo

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

Pubbl/distr/stampa

Berlin ; ; New York, : De Gruyter, c2011

ISBN

9786613166371

9781283166379

1283166372

9783110250657

3110250659

Edizione

[1st ed.]

Descrizione fisica

1 online resource (152 p.)

Collana

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

Classificazione

510

Altri autori (Persone)

KokurinM. I︠U︡ (Mikhail I︠U︡rʹevich)

SmirnovaA. B (Aleksandra Borisovna)

Disciplina

515/.353

Soggetti

Differential equations, Partial - Improperly posed problems

Iterative methods (Mathematics)

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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.