Department of Mathematics Massachusetts Institute of Technology 
Evaluations:  Current students: Please submit the online evaluations before Sunday, December 16.  

Description:  Advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of Matlab.  
Lecturer:  PerOlof Persson, Room 2363A, Phone 6172534989, Email persson 'at' mit.edu, Office hours Tue 23pm in Room 2363A.  
Lectures:  Room 1390, MW 9:3011  
Teaching Assistant:  Anshul Mohnot, Email anshulm 'at' mit.edu, Office hours Mon 45pm in Room 34301.  
Textbook: 
[NLA] Numerical Linear Algebra, Trefethen and Bau, SIAM 1997
(Books24x7 (MIT only), Lecture 15 Online, Quantum Books, Amazon, SIAM) 

Other Readings: 
[Eig] Templates for the Solution of Algebraic Eigenvalue Problems: a Practical Guide, Bai et al, SIAM 2000
(HTML) [It] Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, Barrett et al, SIAM 1993 (PS, HTML) [CG] An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, Jonathan R. Shewchuk, August 1994 (PS, PDF) [FP] What Every Computer Scientist Should Know About Floating Point Arithmetic, David Goldberg, ACM Computing Surveys, 1991 (CiteSeer) Iterative KrylovSubspace Solvers, Sivan Toledo (Lecture 21) (PDF) Lecture slides will be provided on the course webpages 

Grading:  Homework assignments (60%), Midterm (40%)  
Other webpages: 
Stellar (announcements, homework submissions, etc) Fall 2006, Lecturer PerOlof Persson (Math, Stellar, OCW) Fall 2005, Lecturer PerOlof Persson (Math, Stellar) Fall 2004, Lecturer Plamen Koev (Math, OCW) Fall 2001, Lecturer Dan Stefanica (Math) 

Other links: 
MIT 18.06 Linear Algebra (for Linear Algebra review) The MIT CDO Program (Computation for Design and Optimization, this class is one of the four core subjects) The algorithm for MATLAB's backslash operator (from The Mathworks Online Documentation) 

Policies, etc: 
Please start early with the homeworks, it might be hard to get
help the last few days before they are due. Solutions will be given out
soon after the due date; therefore there will be no extensions.
Collaboration on the homeworks is encouraged, but each student must write his/her own solutions, understand all the details of them, and be prepared to answer questions about them. No books, notes, or calculators are allowed on the Midterm exam. 

Exams: 
Midterm: Wednesday, Nov 7 (inclass: 9:30am11:00am).
No books, notes, or calculators are allowed on the Midterm exam. The midterm will cover:


Homework: 


Syllabus: 
NLA 38, Sh


MATLAB Codes: 
Lecture 2, Vector Norms (lec2mldemo1.m), Induced Matrix Norms (lec2mldemo2.m) Lecture 5, Classical and Modified GramSchmidt (lec5mldemo1.m, clgs.m, mgs.m) Lecture 6, Householder QR Factorization (house.m, formQ.m) Lecture 8, Floating Point Arithmetic (lec8mldemo1.m, num2bin.m) Lecture 11, LU Factorization (lec11mldemo1.m, lec11mldemo2.m, mkL.m, mkP.m) Homework 4, Banded Cholesky (bandtest.m) Lecture 16, Jacobi Algorithm (lec16mldemo1.m, jacrot.m) Lecture 17, Method of Bisection (lec17mldemo1.m, sturmcount.m), DivideandConquer Algorithm (lec17mldemo2.m) Homework 5, Linear Elasticity Utilities (assemble.m, elmatrix.m, mkmodel.m, qdplot.m, qdanim.m, allhw5.zip) Lecture 19, Conjugate Gradients (cg.m, cg_stats.m) Lecture 20, Elimination Movie (lec20mldemo1.m, realmmd.m) Lecture 22, Conjugate Gradients (lec22mldemo1.m, steep.m, conjdir.m, conjgrad.m) Lecture 23, Arnoldi Iteration (arnoldi.m) 