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<TITLE>B573, Section 1179: Scientific Computing II</TITLE><body bgcolor="#ffffe0"><H2>B573: Scientific Computing II</H2><DL><DD> Iterative Solution of Large Scale Systems - Fall 1996<DD> B573, Section 1179<DD> 2:00-3:20PM, MW<DD> 115 Lindley Hall</DL><H4>Contents</H4><UL><LI> <!WA0><A HREF="#general">General information</A><LI> <!WA1><A HREF="#description">Course description</A><LI> <!WA2><A HREF="#outline">Tentative course outline</A><LI> <!WA3><A HREF="#assignments">Assignments</A><LI> <!WA4><A HREF="#grading">Grading policies</A><LI> <!WA5><A HREF="#lectures">Lecture notes</A></UL><HR><A NAME="general"><H2>General Information</H2></A><DL><DT> Instructor:<UL><li><ADDRESS><!WA6><A HREF="http://www.cs.indiana.edu/hyplan/bramley.html">Randall Bramley</A> /<!WA7><A HREF="mailto:bramley@cs.indiana.edu">bramley@cs.indiana.edu</A></ADDRESS><li> email: <EM>bramley.cs.indiana.edu</EM><li> 301A Lindley Hall</UL><DT> Prerequisites:<DD>  Mathematics M343 and one of M303 or M301, and a working knowledge of Fortran, C, or C++.Students should be able to write and run programs under a UNIX operating system.<DT> Textbook:<DD> <EM> Iterative Methods for Sparse Linear Systems </EM> by Yousef Saad. <BR>  This is intended as a reference work, and the material covered in thiscourse is not identical to that in the textbook.</DL> <H3>Office Hours</H3>Same as on the home page:  Mon - Wed, 9:00 - 10:00 AM.<A NAME="description"><H3>Course Description</H3></A>This course is for students in the sciences and applied mathematics whose research involves solvinglarge sparse linear systems on a computer, and for computer scientists interested in learningthe computational problems encountered in scientific and engineering codes.Sparse linear systems occur in most large scale physical modelingprograms and often the setting up and solution of them accounts for the majority of the computer time.This course will focus on practical methods and their computer implementation,with a minimal amount of the underlying mathematical theory.  High level tools will be used in order to quickly implement and test methods.Existing software will also be used whenever possible,to avoid building everything from scratch, and to learn how to use existing software resources.Course goals include the ability to understand the influence of computerarchitecture on the choice of methods and data structures,the strengths and weaknesses of basic methods, common sources of large sparse linear systems,and the resulting implications for choosing methods and implementations.Students will finish the semester with a toolkit of solvers that they canthen use for solving scientific problems, for probing computer architectures, orfor obtaining a deeper understanding of the methods commonly used inscientific computing.<HR><A NAME="outline"><H3>Tentative Course Outline</H3></A><UL><li> A quick start: everything you knew about solving linear systems from your linear algebra course.<li> Introduction     <UL>        <li> Basic linear algebra you haven't seen before        <li> Sources of large sparse linear systems        <li> Computer architecture basics        <li> Data structures and stopping tests     </UL><li> Iterative methods: pre-1972 technology     <UL>        <li> Linear stationary        <li> Conjugate gradients (CG): theory        <li> CG convergence properties        <li> Preconditioning CG     </UL><li> Computational kernels and software resources     <UL>        <li> Expressing iterative methods in terms of  kernel operations        <li> Toolkits for sparse system manipulations: Sparskit,  Sparse BLAS        <li> Packages:  PetsC, Aztec, SPLIB, Templates        <li> Finding and using numerical software from the Net     </UL><li> Iterative methods: recent technology     <UL>        <li> Basic derivation ideas: orthogonalization, restarts, truncation        <li> CG on normal equations        <li> Generalized Conjugate Residuals, Orthomin(m), GCR(m)        <li> Generalized Minimal Residuals, GMRES(m)        <li> Bi-conjugate gradients, CG-squared, CG-Stab, QMR     </UL><li> Preconditioning and related ideas     <UL>        <li> Scaling/equilibration        <li> Incomplete factorization        <li> Polynomial methods and preconditioning        <li> Other "preconditioning" methods     </UL><li> Crafting a solution strategy     <UL>        <li> Choice of solvers        <li> Choice of preconditioners        <li> Choice of stopping test(s)        <li> Reading  the literature: judicious use of a jaundiced eye     </UL> </UL> <HR><A NAME="Newsgroup"><H3>Class Newsgroup</H3></A>The course newsgroup, <!WA8><A NAME=1 HREF="news:ac.csci.b573">ac.csci.b573</A>, will beused to post announcements, assignments, corrections, and any exceptionsto usual office hours.  Use it to postquestions related to the course or share related information with theclass.  You are responsible for checking the newsgroup frequently, sinceany changes or corrections to assignments will appear there.<A NAME="grading"><H3>Grading Policies</H3></A>Grades are based on projects involving writing and/or analyzing computer programs.Written reports are required for these projects.Each assignment will have questions intended to begin your thinking process,not end it.  Grading will also be based on the questions you raise and answer in these projects.For example, if the question is "Which of the methods A and B is faster,"simply saying "A" is not sufficient.  You should also ask the underlyingquestion ``What measure of fast is appropriate here?'',  "Why is A faster?", etc.Most projects you can tackle in groups.  However, you must give full attribution for any outside sources you use for ideas, software, or help.Also, I reserve the right to call on any member of the group topresent/explain/defend/justify the group's work and to base theentire group's grade on that member's performance.  So be careful who you team up with!<H4>Cheating</H4>Don't.  You can get away with virtually any lifting or scavenging of material,provided you cite the source.  If your citation is "I photocopied another student'swrite-up" then you won't get many points on the assignment, but at least youwon't be branded with a scarlet "P" and tarred and feathered.<HR><A NAME="assignments"><H3>Assignments</H3></A>Assignments will be given often; a total of 10-15 willbe given (depending on the chunk size of each one!).<UL> <LI> <!WA9><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex1.ps"> Assignment 1</A><LI> <!WA10><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex2.ps"> Assignment 2</A><LI> <!WA11><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex3.ps"> Assignment 3</A><LI> <!WA12><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex4.ps"> Assignment 4</A>Be sure to make the modifications that were specified in class lecture,designed to make your life easier!<LI> <!WA13><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex5.ps"> Assignment 5</A><LI> <!WA14><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex6.ps"> Assignment 6</A> on GMRES(m).<LI> <!WA15><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex7.ps"> Assignment 7</A> on projectors.<LI> <!WA16><A HREF="http://www.cs.indiana.edu/scicomp/b573/ex8.ps"> Assignment 8</A> on the composite stepCGSTAB algorithm of Chan and Szeto.</UL><HR><A NAME="lectures"><H3>Lecture Notes</H3></A>This is not a full or complete set of lecture notes; in thewords of a not-so-great philosopher, "You had to be there".If you miss a lecture,be sure to check with other students in the class for what went on.These are in Postscript, since latex2html still is not up to snufffor papers with lots of math symbols.<UL> <LI> <!WA17><A HREF="http://www.cs.indiana.edu/scicomp/b573/conv.ps">Conventions and Notation</A><LI> <!WA18><A HREF="http://www.cs.indiana.edu/scicomp/b573/class.ps">Classifications of Problems and Methods</A><LI> <!WA19><A HREF="http://www.cs.indiana.edu/scicomp/b573/origins.ps">Origins of Linear Problems</A><LI> <!WA20><A HREF="http://www.cs.indiana.edu/scicomp/b573/memory.ps">Memory Systems and Performance</A><LI> <!WA21><A HREF="http://www.cs.indiana.edu/scicomp/b573/pipelining.ps">Pipelining and Performance</A><LI> <!WA22><A HREF="http://www.cs.indiana.edu/scicomp/b573/blas.html">The BLAS</A><LI> <!WA23><A HREF="http://www.cs.indiana.edu/scicomp/b573/ds.ps">Sparse Matrix Data Structures</A><LI> <!WA24><A HREF="http://www.cs.indiana.edu/scicomp/b573/cg0.ps">Conjugate Gradient Algorithm: Part 0</A><LI> <!WA25><A HREF="http://www.cs.indiana.edu/scicomp/b573/ls.ps">Linear Stationary Methods</A><LI> <!WA26><A HREF="http://www.cs.indiana.edu/scicomp/b573/cheby.ps">Chebyshev Method and Residual Polynomials</A><LI> <!WA27><A HREF="http://www.cs.indiana.edu/scicomp/b573/cg.ps">Conjugate Gradient Algorithm: Part 1</A><LI> <!WA28><A HREF="http://www.cs.indiana.edu/scicomp/b573/tools.html">Toolboxs for Iterative Methods</A><LI> <!WA29><A HREF="http://www.cs.indiana.edu/scicomp/b573/iccg.ps">Preconditioning: CG</A><LI> <!WA30><A HREF="http://www.cs.indiana.edu/scicomp/b573/leastsq.ps">Least Squares Problems and Algorithms</A><LI> <!WA31><A HREF="http://www.cs.indiana.edu/scicomp/b573/meth1.ps">Nonsymmetric Methods I: GCR, Orthomin, GMRES</A><LI> <!WA32><A HREF="http://www.cs.indiana.edu/scicomp/b573/precond.ps">Preconditioning: Nonsymmetric Solvers</A><LI> <!WA33><A HREF="http://www.cs.indiana.edu/scicomp/b573/matlab.html">MATLAB Information</A><LI> <!WA34><A HREF="http://www.cs.indiana.edu/scicomp/b573/proj.ps">Projectors, Lanczos Algorithm, and Bi-CG Methods</A><LI> <!WA35><A HREF="http://www.cs.indiana.edu/scicomp/b573/iter.eps">An Idiosyncratic View of Nonsymmetric Solvers</A><LI> <!WA36><A HREF="http://www.cs.indiana.edu/scicomp/b573/perm.eps">Basic Matrix Reordering</A></UL>
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