网站综合信息 cme324.stanford.edu
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网址:http://cme324.stanford.edu/
标题:CS 336/CME 324 Spring '06 Home Page
关键字:Stanford, CME 324, CS 339, Numerical Linear Algebra, Matrix Computations,
描述:CME 324/CS 336. Advanced Methods in Matrix Computations: Iterative Methods Institute for Computational and Mathematical Engineering and the Department of Computer Science Stanford University Spring 20
主体:
网址:http://cme324.stanford.edu/
标题:CS 336/CME 324 Spring '06 Home Page
关键字:Stanford, CME 324, CS 339, Numerical Linear Algebra, Matrix Computations,
描述:CME 324/CS 336. Advanced Methods in Matrix Computations: Iterative Methods Institute for Computational and Mathematical Engineering and the Department of Computer Science Stanford University Spring 20
主体:
CME 324/CS 336. Advanced Methods in Matrix Computations: Iterative MethodsInstitute for Computational and Mathematical Engineeringand the Department of Computer ScienceStanford UniversitySpring 2006This is a course on Matrix Computations with emphasis on iterative methods for solving linear systems. The course will include such methods as the Conjugate Gradient Method and GMRES. There will be some discussion of eigenvalue methods too. Prerequisite: CME 302/CS 237A. Numerical Linear Algebra.Announcements05/17/06: Instructions for term paper have been posted.05/21/06: There will not be a lecture on Friday, May 26.05/16/06: Problem 3 added to Problem Set 2. Please see updated file below.05/11/06: Problem Set 2 has been posted.05/10/06: There will be lectures on the following Fridays: May 12, 19 & 26. The last day of class is May 26.04/19/06: Problem Set 1 has been posted.04/10/06: Future classes will be held in Gates 100 instead of Gates 260.04/06/06: Please send Lek-Heng an e-mail if you are not registered for the class but want your e-mail to be included in the class mailing list.04/05/06: There will be no Friday lectures unless announced otherwise.LecturesLocation: Gates Building, Room 100Times: 11:00 AM–12:15 PM on Mon/WedCourse staffInstructor: Gene Golub (golub@stanford.edu).Gates Building 2B, Room 280(650) 723-3124Office hours by appointment.Teaching assistant: Lek-Heng Lim (lekheng@stanford.edu).Gates Building 2B, Room 286(650) 723-4101Office hours by appointment.TopicsIntroductionSparse and structured matricesModel problem: Poisson equationStationary MethodsSOR: Successive overrelaxationSSOR: Symmetric SORProperty ACheckerboard/red-black orderingBlock methodsChebyshev polynomialsLebedev-Finogenov parameter orderingRegular splittingOstrowski theoremSplitting and preconditioningChebyshev semi-iterative methodChebyshev accleration and CGForsythe-Straus theoremFast Poisson solverDomain decompositionIncomplete factorizationBanded and block-tridiagonal matricesM matrixMeijerink-van der Vorst theoremKKT systemsReal positive matricesAdditive polar decompositionCayley transformComplex symmetric matricesArrow-Hurwitz-Uzawa algorithmKrylov Subspace MethodsSteepest descentKantorovich inequalityCG: conjugate gradient methodPreconditioned CG from Chebyshev accelerationClassical CG methodLanczos tridiagonalizationUnsymmetric and singular systemsLeast squares problemsGolub-Kahan bidiagonalizationPaige-Saunders LSQRSaad-Schultz GMRES: generalized minimal residualUnsymmetric Lanczos tridiagonalizationBiCG methodParlett's look-ahead strategiesFreund-Nachtigal QMR: quasi-minimal residualOther TopicsMomentsQuadrature: Gauss, Gauss-Radau, Gauss-LobattoStieljes integralsOrthogonal polynomialsEstimating values of bilinear forms of analytic functions of symmetric matricesLecture notes, etcLecture notes (posted: 04/26/06)Lecture 14 (05/17/06):Transcript (posted: 05/18/06)Lecture 13 (05/15/06):Transcript (posted: 05/18/06)C.C. Paige and M.A. Saunders, "Solution
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