LEADER 04049nam 2200757 a 450 001 9910813312003321 005 20240516053052.0 010 $a1-283-16637-2 010 $a9786613166371 010 $a3-11-025065-9 024 7 $a10.1515/9783110250657 035 $a(CKB)2550000000035152 035 $a(EBL)689697 035 $a(OCoLC)732957489 035 $a(SSID)ssj0000530393 035 $a(PQKBManifestationID)12214274 035 $a(PQKBTitleCode)TC0000530393 035 $a(PQKBWorkID)10562197 035 $a(PQKB)11146259 035 $a(MiAaPQ)EBC689697 035 $a(DE-B1597)122988 035 $a(OCoLC)768164686 035 $a(OCoLC)840443085 035 $a(DE-B1597)9783110250657 035 $a(Au-PeEL)EBL689697 035 $a(CaPaEBR)ebr10468344 035 $a(CaONFJC)MIL316637 035 $a(EXLCZ)992550000000035152 100 $a20100927d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIterative methods for ill-posed problems $ean introduction /$fAnatoly B. Bakushinsky, Mikhail Yu. Kokurin, Alexandra Smirnova 205 $a1st ed. 210 $aBerlin ;$aNew York $cDe Gruyter$dc2011 215 $a1 online resource (152 p.) 225 1 $aInverse and ill-posed problems series,$x1381-4524 ;$v54 300 $aDescription based upon print version of record. 311 $a3-11-025064-0 320 $aIncludes bibliographical references and index. 327 $t Frontmatter -- $tPreface -- $tContents -- $t1 The regularity condition. Newton's method -- $t2 The Gauss-Newton method -- $t3 The gradient method -- $t4 Tikhonov's scheme -- $t5 Tikhonov's scheme for linear equations -- $t6 The gradient scheme for linear equations -- $t7 Convergence rates for the approximation methods in the case of linear irregular equations -- $t8 Equations with a convex discrepancy functional by Tikhonov's method -- $t9 Iterative regularization principle -- $t10 The iteratively regularized Gauss-Newton method -- $t11 The stable gradient method for irregular nonlinear equations -- $t12 Relative computational efficiency of iteratively regularized methods -- $t13 Numerical investigation of two-dimensional inverse gravimetry problem -- $t14 Iteratively regularized methods for inverse problem in optical tomography -- $t15 Feigenbaum's universality equation -- $t16 Conclusion -- $tReferences -- $tIndex 330 $aIll-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces. 410 0$aInverse and ill-posed problems series ;$vv. 54. 606 $aDifferential equations, Partial$xImproperly posed problems 606 $aIterative methods (Mathematics) 610 $aHilbert Space. 610 $aIll-posed Problem. 610 $aInverse Problem. 610 $aIterative Method. 610 $aOperator Equation. 615 0$aDifferential equations, Partial$xImproperly posed problems. 615 0$aIterative methods (Mathematics) 676 $a515/.353 686 $a510$2GyFmDB 700 $aBakushinskii?$b A. B$g(Anatolii? Borisovich)$031864 701 $aKokurin$b M. I?U$g(Mikhail I?Ur?evich)$01597293 701 $aSmirnova$b A. B$g(Aleksandra Borisovna)$01597294 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910813312003321 996 $aIterative methods for ill-posed problems$93919000 997 $aUNINA