國立虎尾科技大學 |

Saddle-Point Problems and Their Iterative Solution

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Saddle-Point Problems and Their Iterative Solution/ by Miroslav Rozložník.
作者:	Rozložník, Miroslav.
面頁冊數:	XIV, 136 p. 37 illus., 12 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Numerical analysis. -
電子資源:	https://doi.org/10.1007/978-3-030-01431-5
ISBN:	9783030014315

Saddle-Point Problems and Their Iterative Solution
Rozložník, Miroslav.

Saddle-Point Problems and Their Iterative Solution[electronic resource] /by Miroslav Rozložník. - 1st ed. 2018. - XIV, 136 p. 37 illus., 12 illus. in color.online resource. - Nečas Center Series,2523-3343. - Nečas Center Series,.

Introductory 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.

This 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.

ISBN: 9783030014315

Standard No.: 10.1007/978-3-030-01431-5doiSubjects--Topical Terms:

527939
Numerical analysis.

LC Class. No.: QA297-299.4

Dewey Class. No.: 518

Saddle-Point Problems and Their Iterative Solution
LDR:03199nam a22003975i 4500 001 990097
003 DE-He213
005 20200704004621.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783030014315 $9 978-3-030-01431-5
024 7 $a 10.1007/978-3-030-01431-5 $2 doi
035 $a 978-3-030-01431-5
050 4 $a QA297-299.4
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 518 $2 23
100 1 $a Rozložník, Miroslav. $e editor. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1267765
245 1 0 $a Saddle-Point Problems and Their Iterative Solution $h [electronic resource] / $c by Miroslav Rozložník.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2018.
300 $a XIV, 136 p. 37 illus., 12 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Nečas Center Series, $x 2523-3343
505 0 $a Introductory 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.
520 $a This 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.
650 0 $a Numerical analysis. $3 527939
650 1 4 $a Numerical Analysis. $3 671433
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030014308
776 0 8 $i Printed edition: $z 9783030014322
830 0 $a Nečas Center Series, $x 2523-3343 $3 1280950
856 4 0 $u https://doi.org/10.1007/978-3-030-01431-5
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)