04049nam 2200757 a 450 991081331200332120240516053052.01-283-16637-297866131663713-11-025065-910.1515/9783110250657(CKB)2550000000035152(EBL)689697(OCoLC)732957489(SSID)ssj0000530393(PQKBManifestationID)12214274(PQKBTitleCode)TC0000530393(PQKBWorkID)10562197(PQKB)11146259(MiAaPQ)EBC689697(DE-B1597)122988(OCoLC)768164686(OCoLC)840443085(DE-B1597)9783110250657(Au-PeEL)EBL689697(CaPaEBR)ebr10468344(CaONFJC)MIL316637(EXLCZ)99255000000003515220100927d2011 uy 0engur|n|---|||||txtccrIterative methods for ill-posed problems an introduction /Anatoly B. Bakushinsky, Mikhail Yu. Kokurin, Alexandra Smirnova1st ed.Berlin ;New York De Gruyterc20111 online resource (152 p.)Inverse and ill-posed problems series,1381-4524 ;54Description based upon print version of record.3-11-025064-0 Includes bibliographical references and index. 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 -- IndexIll-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. Inverse and ill-posed problems series ;v. 54.Differential equations, PartialImproperly posed problemsIterative methods (Mathematics)Hilbert Space.Ill-posed Problem.Inverse Problem.Iterative Method.Operator Equation.Differential equations, PartialImproperly posed problems.Iterative methods (Mathematics)515/.353510GyFmDBBakushinskiĭ A. B(Anatoliĭ Borisovich)31864Kokurin M. I͡U(Mikhail I͡Urʹevich)1597293Smirnova A. B(Aleksandra Borisovna)1597294MiAaPQMiAaPQMiAaPQBOOK9910813312003321Iterative methods for ill-posed problems3919000UNINA