LEADER 04034nam 22005295 450 001 9910863181703321 005 20251113203954.0 010 $a9783030552510 010 $a3030552519 024 7 $a10.1007/978-3-030-55251-0 035 $a(CKB)4100000011479498 035 $a(DE-He213)978-3-030-55251-0 035 $a(MiAaPQ)EBC6362812 035 $a(PPN)255204035 035 $a(MiAaPQ)EBC6362691 035 $a(EXLCZ)994100000011479498 100 $a20201002d2020 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKrylov Methods for Nonsymmetric Linear Systems $eFrom Theory to Computations /$fby Gérard Meurant, Jurjen Duintjer Tebbens 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XIV, 686 p. 184 illus.) 225 1 $aSpringer Series in Computational Mathematics,$x2198-3712 ;$v57 311 08$a9783030552503 311 08$a3030552500 320 $aIncludes bibliographical references and index. 327 $a1. Notation, definitions and tools -- 2. Q-OR and Q-MR methods -- 3. Bases for Krylov subspaces -- 4. FOM/GMRES and variants -- 5. Methods equivalent to FOM or GMRES- 6. Hessenberg/CMRH -- 7. BiCG/QMR and Lanczos algorithms -- 8. Transpose-free Lanczos methods -- 9. The IDR family -- 10. Restart, deflation and truncation -- 11. Related topics -- 12. Numerical comparison of methods -- A. Test matrices and short biographical notices -- References -- Index. 330 $aThis book aims to give an encyclopedic overview of the state-of-the-art of Krylov subspace iterative methods for solving nonsymmetric systems of algebraic linear equations and to study their mathematical properties. Solving systems of algebraic linear equations is among the most frequent problems in scientific computing; it is used in many disciplines such as physics, engineering, chemistry, biology, and several others. Krylov methods have progressively emerged as the iterative methods with the highest efficiency while being very robust for solving large linear systems; they may be expected to remain so, independent of progress in modern computer-related fields such as parallel and high performance computing.The mathematical properties of the methods are described and analyzed along with their behavior in finite precision arithmetic. A number of numerical examples demonstrate the properties and the behavior of the described methods. Also considered are the methods? implementations and coding as Matlab®-like functions. Methods which became popular recently are considered in the general framework of Q-OR (quasi-orthogonal )/Q-MR (quasi-minimum) residual methods. This book can be useful for both practitioners and for readers who are more interested in theory. Together with a review of the state-of-the-art, it presents a number of recent theoretical results of the authors, some of them unpublished, as well as a few original algorithms. Some of the derived formulas might be useful for the design of possible new methods or for future analysis. For the more applied user, the book gives an up-to-date overview of the majority of the available Krylov methods for nonsymmetric linear systems, including well-known convergence properties and, as we said above, template codes that can serve as the base for more individualized and elaborate implementations. 410 0$aSpringer Series in Computational Mathematics,$x2198-3712 ;$v57 606 $aNumerical analysis 606 $aNumerical Analysis 615 0$aNumerical analysis. 615 14$aNumerical Analysis. 676 $a512.5 700 $aMeurant$b Ge?rard A.$0431205 702 $aDuintjer Tebbens$b Jurjen 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910863181703321 996 $aKrylov methods for nonsymmetric linear systems$92287946 997 $aUNINA