LEADER 01181nam0 22003133i 450 001 UMC0427118 005 20231121125912.0 010 $a0937058580 100 $a20191004d2002 ||||0itac50 ba 101 | $aeng 102 $aus 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $aVia crucis$eessays on early medieval sources and ideas in memory of J. E. Cross$fedited by Thomas N. Hall$gwith assistance from Thomas D. Hill & Charles D. Wright 210 $aMorgantown$cWest Virginia university press$d©2002 215 $aXVII, 449 p.$d23 cm. 225 | $aMedieval European studies$v1 410 0$1001UBO1843066$12001 $aMedieval European studies$v1 702 1$aHall$b, Thomas N.$3PUVV180414 702 1$aWright$b, Charles D.$3UFIV084361 702 1$aHill$b, Thomas D.$3UFIV123350 801 3$aIT$bIT-01$c20191004 850 $aIT-FR0017 899 $aBiblioteca umanistica Giorgio Aprea$bFR0017 $eN 912 $aUMC0427118 950 0$aBiblioteca umanistica Giorgio Aprea$d 52MAG 4/649$e 52LLC0000019695 VMN RS $fA $h20191004$i20191004 977 $a 52 996 $aVia Crucis$93603795 997 $aUNICAS LEADER 03805nam 22006735 450 001 9910544877303321 005 20251113211409.0 010 $a3-030-88159-8 024 7 $a10.1007/978-3-030-88159-7 035 $a(MiAaPQ)EBC6886987 035 $a(Au-PeEL)EBL6886987 035 $a(CKB)21167558900041 035 $a(PPN)26082576X 035 $a(OCoLC)1302008344 035 $a(DE-He213)978-3-030-88159-7 035 $a(EXLCZ)9921167558900041 100 $a20220210d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInverse Linear Problems on Hilbert Space and their Krylov Solvability /$fby Noč Angelo Caruso, Alessandro Michelangeli 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (150 pages) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$aPrint version: Caruso, Noč Angelo Inverse Linear Problems on Hilbert Space and Their Krylov Solvability Cham : Springer International Publishing AG,c2022 9783030881580 320 $aIncludes bibliographical references and index. 327 $aIntroduction and motivation -- Krylov solvability of bounded linear inverse problems -- An analysis of conjugate-gradient based methods with unbounded operators -- Krylov solvability of unbounded inverse problems -- Krylov solvability in a perturbative framework -- Outlook on general projection methods and weaker convergence -- References -- Index. 330 $aThis book presents a thorough discussion of the theory of abstract inverse linear problems on Hilbert space. Given an unknown vector f in a Hilbert space H, a linear operator A acting on H, and a vector g in H satisfying Af=g, one is interested in approximating f by finite linear combinations of g, Ag, A2g, A3g, ? The closed subspace generated by the latter vectors is called the Krylov subspace of H generated by g and A. The possibility of solving this inverse problem by means of projection methods on the Krylov subspace is the main focus of this text. After giving a broad introduction to the subject, examples and counterexamples of Krylov-solvable and non-solvable inverse problems are provided, together with results on uniqueness of solutions, classes of operators inducing Krylov-solvable inverse problems, and the behaviour of Krylov subspaces under small perturbations. An appendix collects material on weaker convergence phenomena in general projection methods. This subject of this book lies at the boundary of functional analysis/operator theory and numerical analysis/approximation theory and will be of interest to graduate students and researchers in any of these fields. . 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aDifferential equations 606 $aFunctional analysis 606 $aNumerical analysis 606 $aOperator theory 606 $aDifferential Equations 606 $aFunctional Analysis 606 $aNumerical Analysis 606 $aOperator Theory 615 0$aDifferential equations. 615 0$aFunctional analysis. 615 0$aNumerical analysis. 615 0$aOperator theory. 615 14$aDifferential Equations. 615 24$aFunctional Analysis. 615 24$aNumerical Analysis. 615 24$aOperator Theory. 676 $a515.357 676 $a515.357 700 $aNoe? Angelo Caruso$01258925 702 $aMichelangeli$b Alessandro 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910544877303321 996 $aInverse Linear Problems on Hilbert Space and their Krylov Solvability$94464265 997 $aUNINA