LEADER 03397nam 22004815 450 001 9910300125303321 005 20200704004621.0 010 $a3-030-01431-2 024 7 $a10.1007/978-3-030-01431-5 035 $a(CKB)4100000007159009 035 $a(DE-He213)978-3-030-01431-5 035 $a(MiAaPQ)EBC6230074 035 $a(PPN)232472939 035 $a(EXLCZ)994100000007159009 100 $a20181119d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSaddle-Point Problems and Their Iterative Solution /$fby Miroslav Rozlo?ník 205 $a1st ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (XIV, 136 p. 37 illus., 12 illus. in color.) 225 1 $aNe?as Center Series,$x2523-3343 311 $a3-030-01430-4 327 $aIntroductory remarks. Formulation of saddle-point problem -- Applications leading to saddle-point problems. Augmented systems in least squares problems. Saddle point problems from the discretization of partial differential equations with constraints. Kuhn-Karush-Tucker (KKT) systems in interior-point methods -- Properties of saddle point matrices. The inverse of a saddle-point matrix. Spectral properties of saddle-point matrices -- Solution approaches for saddle-point problems. Schur complement reduction. Null-space projection method -- Direct methods for symmetric indefinite systems. Direct solution of saddle-point problems -- AIterative solution of saddle-point problems. Stationary iteration methods. Krylov subspace methods. Preconditioned Krylov subspace methods -- Saddle-point preconditioners. Block diagonal and triangular preconditioners. Indefinite preconditioning -- Implementation and numerical behavior of saddle-point solvers -- Case study: Polluted undeground water flow modelling in porous media. 330 $aThis book provides essential lecture notes on solving large linear saddle-point systems, which arise in a wide range of applications and often pose computational challenges in science and engineering. The focus is on discussing the particular properties of such linear systems, and a large selection of algebraic methods for solving them, with an emphasis on iterative methods and preconditioning. The theoretical results presented here are complemented by a case study on potential fluid flow problem in a real world-application. This book is mainly intended for students of applied mathematics and scientific computing, but also of interest for researchers and engineers working on various applications. It is assumed that the reader has completed a basic course on linear algebra and numerical mathematics. 410 0$aNe?as Center Series,$x2523-3343 606 $aNumerical analysis 606 $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050 615 0$aNumerical analysis. 615 14$aNumerical Analysis. 676 $a519.4 676 $a518 700 $aRozlo?ník$b Miroslav$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767890 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300125303321 996 $aSaddle-Point Problems and Their Iterative Solution$91563748 997 $aUNINA