03095nam 2200541 450 991046600120332120200923020339.03-11-049805-73-11-049946-010.1515/9783110499469(CKB)3710000001177226(MiAaPQ)EBC4843236(DE-B1597)470629(OCoLC)984647843(DE-B1597)9783110499469(Au-PeEL)EBL4843236(CaPaEBR)ebr11375535(CaONFJC)MIL1006393(OCoLC)983733377(EXLCZ)99371000000117722620170505h20172017 uy 0engurcnu||||||||rdacontentrdamediardacarrierInterval analysis and automatic result verification /Günter MayerBerlin, [Germany] ;Boston, [Massachusetts] :De Gruyter,2017.©20171 online resource (518 pages)De Gruyter Studies in Mathematics,0179-0986 ;Volume 653-11-050063-9 Includes bibliographical references and indexes.Frontmatter -- Preface -- Contents -- 1. Preliminaries -- 2. Real intervals -- 3. Interval vectors, interval matrices -- 4. Expressions, P-contraction, ε-inflation -- 5. Linear systems of equations -- 6. Nonlinear systems of equations -- 7. Eigenvalue problems and related ones -- 8. Automatic differentiation -- 9. Complex intervals -- Final Remarks -- Appendix -- A. Proof of the Jordan normal form -- B. Two elementary proofs of Brouwer's fixed point theorem -- C. Proof of the Newton-Kantorovich Theorem -- D. Convergence proof of the row cyclic Jacobi method -- E. The CORDIC algorithm -- F. The symmetric solution set - a proof of Theorem 5.2.6 -- G. A short introduction to INTLAB -- Bibliography -- Symbol Index -- Author Index -- Subject IndexThis 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, ε-inflation Linear systems of equations Nonlinear systems of equations Eigenvalue problems Automatic differentiation Complex intervalsDe Gruyter studies in mathematics ;Volume 65.Interval analysis (Mathematics)Electronic books.Interval analysis (Mathematics)511.42Mayer Günter171361MiAaPQMiAaPQMiAaPQBOOK9910466001203321Interval analysis2465137UNINA