03567nam 2200565 i 45000010014000000030005000140050017000190060019000360070015000550080041000700100031001110200030001420200025001720280015001970350025002120350021002370400040002580500024002980820016003221000031003382450100003692640150004693000027006193360021006463370026006673380032006934900025007255040051007505050299008015060072011005201150011725300037023225380036023595380047023955880054024426500021024966500036025176500036025536500020025896530025026096530027026346530025026616530022026866530019027087000034027277100064027617760053028258300027028788560096029059781611974737SIAM20170311133913.0m eo d cr bn |||m|||a170302s2017 pau ob 001 0 eng d a 2016054562z 2016053335 a9781611974737qelectronic z9781611974720qprint50aSL03bSIAM a(CaBNVSL)gtp00566902 a(OCoLC)964624769 aCaBNVSLbengerdacCaBNVSLdCaBNVSL 4aQA402b.O686 2017eb04a003/.742231 aOrban, Dominique,eauthor.10aIterative solution of symmetric quasi-definite linear systems /cDominique Orban, Mario Arioli. 1aPhiladelphia, Pennsylvania :bSociety for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104),c[2017] a1 PDF (xii, 93 pages). atext2rdacontent aelectronic2isbdmedia aonline resource2rdacarrier1 aSIAM spotlights ;v3 aIncludes bibliographical references and index.0 aPreface -- 1. Introduction -- 2. Preliminaries -- 3. Overview of existing direct and iterative methods -- 4. Fundamental processes -- 5. Iterative methods based on reduced equations -- 6. Full-space iterative methods -- 7. Software and numerical experiments -- 8. Discussion and open questions. aRestricted to subscribers or individual electronic text purchasers.3 aNumerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure. This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia. The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages. aAlso available in print version. aMode of access: World Wide Web. aSystem requirements: Adobe Acrobat Reader. aDescription based on title page of print version. 0aSystem analysis. 0aIterative methods (Mathematics) 0aDifferential equations, Linear. 0aLinear systems. aSaddle-point systems aQuasi-definite systems aLinear least squares aIterative methods aKrylov methods1 aArioli, M.q(Mario),eauthor.2 aSociety for Industrial and Applied Mathematics,epublisher.08iPrint version:w(DLC) 2016053335z9781611974720 0aSIAM spotlights ;v03.403SIAMuhttp://epubs.siam.org/doi/book/http://epubs.siam.org/doi/book/10.1137/1.9781611974737