LEADER 04321nam 2200805Ia 450 001 9910807973003321 005 20200520144314.0 010 $a1-280-86872-4 010 $a9786610868728 010 $a1-4294-2711-6 010 $a90-474-1194-3 010 $a3-11-019530-5 024 7 $a10.1515/9783110195309 035 $a(CKB)1000000000334694 035 $a(EBL)280869 035 $a(OCoLC)476024769 035 $a(SSID)ssj0000270268 035 $a(PQKBManifestationID)11215260 035 $a(PQKBTitleCode)TC0000270268 035 $a(PQKBWorkID)10261970 035 $a(PQKB)10951620 035 $a(MiAaPQ)EBC280869 035 $a(MiAaPQ)EBC3003907 035 $a(DE-B1597)20128 035 $a(OCoLC)840443336 035 $a(OCoLC)948655874 035 $a(DE-B1597)9783110195309 035 $a(Au-PeEL)EBL3003907 035 $a(CaPaEBR)ebr10171796 035 $a(CaONFJC)MIL86872 035 $a(OCoLC)568022423 035 $a(MiAaPQ)EBC7151833 035 $a(Au-PeEL)EBL7151833 035 $a(EXLCZ)991000000000334694 100 $a20050923d2005 uy 0 101 0 $aeng 135 $aurnn#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aWell-posed, ill-posed, and intermediate problems with applications /$fYu. P. Petrov and V.S. Sizikov 205 $a1st ed. 210 $aLeiden ;$aBoston $cVSP$dc2005 215 $a1 online resource (244 p.) 225 1 $aInverse and ill-posed problems series,$x1381-4524 300 $aDescription based upon print version of record. 311 0 $a90-6764-432-3 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tPreface --$tContents --$tPart I. Three classes of problems in mathematics, physics, and engineering --$tChapter 1. Simplest ill-posed problems --$tChapter 2. Problems intermediate between well- and ill-posed problems --$tChapter 3. Change of sensitivity to measurement errors under integral transformations used in modeling of ships and marine control systems --$tBibliography to Part I --$tPart II. Stable methods for solving inverse problems --$tChapter 4. Regular methods for solving ill-posed problems --$tChapter 5. Inverse problems in image reconstruction and tomography --$tBibliography to Part II --$tIndex 330 $aThis book deals with one of the key problems in applied mathematics, namely the investigation into and providing for solution stability in solving equations with due allowance for inaccuracies in set initial data, parameters and coefficients of a mathematical model for an object under study, instrumental function, initial conditions, etc., and also with allowance for miscalculations, including roundoff errors. Until recently, all problems in mathematics, physics and engineering were divided into two classes: well-posed problems and ill-posed problems. The authors introduce a third class of problems: intermediate ones, which are problems that change their property of being well- or ill-posed on equivalent transformations of governing equations, and also problems that display the property of being either well- or ill-posed depending on the type of the functional space used. The book is divided into two parts: Part one deals with general properties of all three classes of mathematical, physical and engineering problems with approaches to solve them; Part two deals with several stable models for solving inverse ill-posed problems, illustrated with numerical examples. 410 0$aInverse and ill-posed problems series. 606 $aDifferential equations$xNumerical solutions 606 $aNumerical analysis$xImproperly posed problems 606 $aEngineering mathematics 606 $aMathematical physics 615 0$aDifferential equations$xNumerical solutions. 615 0$aNumerical analysis$xImproperly posed problems. 615 0$aEngineering mathematics. 615 0$aMathematical physics. 676 $a515.35 676 $a518/.6 700 $aPetrov$b Yu. P$01700035 701 $aSizikov$b V. S$g(Valerii Sergeevich)$0725438 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910807973003321 996 $aWell-posed, ill-posed, and intermediate problems with applications$94082727 997 $aUNINA