LEADER 03135nam 2200553 450 001 9910792705603321 005 20200923020339.0 010 $a3-11-049805-7 010 $a3-11-049946-0 024 7 $a10.1515/9783110499469 035 $a(CKB)3710000001177226 035 $a(DE-B1597)470629 035 $a(OCoLC)984647843 035 $a(DE-B1597)9783110499469 035 $a(Au-PeEL)EBL4843236 035 $a(CaPaEBR)ebr11375535 035 $a(CaONFJC)MIL1006393 035 $a(OCoLC)983733377 035 $a(CaSebORM)9783110498059 035 $a(MiAaPQ)EBC4843236 035 $a(EXLCZ)993710000001177226 100 $a20170505h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aInterval analysis $eand automatic result verification /$fGu?nter Mayer 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter,$d2017. 210 4$dİ2017 215 $a1 online resource (518 pages) 225 1 $aDe Gruyter Studies in Mathematics,$x0179-0986 ;$vVolume 65 311 $a3-11-050063-9 320 $aIncludes bibliographical references and indexes. 327 $tFrontmatter -- $tPreface -- $tContents -- $t1. Preliminaries -- $t2. Real intervals -- $t3. Interval vectors, interval matrices -- $t4. Expressions, P-contraction, ?-inflation -- $t5. Linear systems of equations -- $t6. Nonlinear systems of equations -- $t7. Eigenvalue problems and related ones -- $t8. Automatic differentiation -- $t9. Complex intervals -- $tFinal Remarks -- $tAppendix -- $tA. Proof of the Jordan normal form -- $tB. Two elementary proofs of Brouwer's fixed point theorem -- $tC. Proof of the Newton-Kantorovich Theorem -- $tD. Convergence proof of the row cyclic Jacobi method -- $tE. The CORDIC algorithm -- $tF. The symmetric solution set - a proof of Theorem 5.2.6 -- $tG. A short introduction to INTLAB -- $tBibliography -- $tSymbol Index -- $tAuthor Index -- $tSubject Index 330 $aThis self-contained text is a step-by-step introduction and a complete overview of interval computation and result verification, a subject whose importance has steadily increased over the past many years. The author, an expert in the field, gently presents the theory of interval analysis through many examples and exercises, and guides the reader from the basics of the theory to current research topics in the mathematics of computation. Contents Preliminaries Real intervals Interval vectors, interval matrices Expressions, P-contraction, ?-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervals 410 0$aDe Gruyter studies in mathematics ;$vVolume 65. 606 $aInterval analysis (Mathematics) 615 0$aInterval analysis (Mathematics) 676 $a511.42 686 $aSK 910$qSEPA$2rvk 700 $aMayer$b Gu?nter$0171361 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910792705603321 996 $aInterval analysis$93752419 997 $aUNINA