Department of Mathematics |

MTH 655 (Numerical Analysis) Large scale scientific computing methods - Winter 2007

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General information Course announcement Textbook and resources Assignments

Assignments/schedule

Date	Schedule/assignment
Monday 1/8	Administration: MANDATORY: fill out questionnaire.html First assignment: Overview - slides Read Chapter 1 from Heath's book Read about numerical analysis disasters by Doug Arnold Read recent discussion in NA-Digest about use of Fortran vs MATLAB in teaching/learning numerical analysis. Use Search Interface and keyword "Fortran"
Wednesday 1/10	No class today. READ material assigned.
Friday 1/12	LAB 1 (MLC Kidd 108J) computer lab. Get the red sheet. Now get the real assignment.
Wednesday 1/17	Newton's method: convergence and variants, read Chapter 5 from [Kelley] and preliminaries, if necessary.
Friday 1/19	LAB 2 (MLC Kidd 108J) computer lab. Unix on Windows=Cygwin Fortran assignment
Monday 1/22	Newton's method in R^N: variants and complexity. Quasi-Newton, inexact Newton. Chord method, approximate Jacobian, FD Jacobian. Factorization methods for solving linear systems. SIGN UP FOR PROJECTS BY FEBRUARY 2
Wednesday 1/24	Applications: linear BVP, nonlinear BVP, Fredholm integral equation. Iterative methods for solving linear systems: splitting methods. Read Chapter 1 from [Kelley].
Friday 1/26	LAB 3 (MLC Kidd 108J) computer lab. Preparation: Please read about `ssh and scp` You must be able to use some text editor under Unix. I suggest emacs or vi. Please look up the basics in Unix reference The assignment is here.
Monday 1/29	Gershgorin theorem. Examples of splittings. Jacobi, Gauss-Seidel, SOR. and Richardson's methods. Start Krylov subspace methods: CG. Read Chapter 2 from [Kelley].
Wednesday 1/31	Steepest descent methods. CG and nonsymmetric variants. GMRES family. Preconditioners: why ! Use relevant demos from this page. Read chapters 3 and 4 from [Kelley].
Friday 2/2	LAB 4 (MLC Kidd 108J) computer lab: continue and finish LAB 3.
Monday 2/5	MULTIGRID 1
Wednesday 2/7	MULTIGRID 2
Friday 2/9	LAB 5 (MLC Kidd 108J): bring your classnotes on iterative solvers.
Monday 2/12	Domain decomposition and parallel computing: introduction
Wednesday 2/14	No class today: read handouts (1 and 3) on performance of computers and on parallel architectures. Make sure you know the following concepts: FLOPS, what comes after teraflops, pipeline, SIMD, MIMD. Solve problems 3.4, 3.12
Friday 2/16	LAB 6 (MLC Kidd 108J): continue LAB 5. Make sure you are ready for LAB 7.
Monday 2/19	Overlapping domain decomposition and parallel implementation of an iterative algorithm (Jacobi and block Jacobi). Notes. Handout with myjacobi_parallel.m
Wednesday 2/21	Basics of MPI and cluster computing. Deadlocks and load balancing. Preparation for LAB 7. Handout 2.
Friday 2/23	LAB 7 (MLC Kidd 108J):
Monday 2/26	Theory of overlapping domain decomposition methods: additive and multiplicative Schwarz.
Wednesday 2/28	Theory of nonoverlapping domain decomposition methods: Schur complement and Steklov-Poincare map.
Friday 3/2	LAB 8: continue LAB 7 (MLC Kidd 108J). Finish other labs.
Monday 3/5	Finish non-overlapping DD algorithms: Dirichlet-Neumann and Neumann-Neumann algorithms.
Wednesday 3/7	Back to nonlinear solvers: globally convergent modifications of Newton algorithm: line search with backtracking, trust region method. Connection to solving minimization problems. Read Chapter 8 form [Kelley].
Friday 3/9	LAB 9: globalized Newton and Newton for optimization (MLC Kidd 108J). Finish other labs.
Monday 3/12	Overview of issues in optimization (constrained, unconstrained), (continuous and discrete). Linear programming, Simulated Annealing, genetic algorithms.
Wednesday 3/14
Friday 3/16	LAB REVIEW: (in class, Gilkey 104) Please bring your lab reports !