| Date | Topic | Handouts | Sources | ||
|---|---|---|---|---|---|
| L1 | Tu | Jan 19 | Introduction | Syllabus & Questionaire | Handout |
| L2 | Th | Jan 21 | Gen. Dirichlet, Review of Lin Alg., Jacobi, Gauss-Seidel | 90.2 "393N Survey of Course" | Handout |
| L3 | Tu | Jan 26 | Direct Sol., Splitting Matrix, SOR | Jan 20, 1990: "Review of Linear Algebra" | Handout |
| L4 | Th | Jan 28 | Model Problem, LDU | "Aprrox. Matrix Factorization" Sup 98.4.14; "Assignment 99.1:Matrix Preliminaries. |
Handout |
| L5 | Tu | Feb 02 | SOR and Applications | 1) "Solvers & SOR" -- sect. 3.3 of AE's dissertation, 2) Summary of Iter. Methods diagram from "Templates". |
Handout |
| L6 | Th | Feb 04 | Choices of Splitting Matrix Q, Convergence, Extrapolation | Pages -1, -2 by Anne, Feb 4, 1999; "Convergence of Basic Iter. Methods" Sup 94.2.22. |
Handout |
| L7 | Tu | Feb 09 | Extrapolation, Variable Extrapolation, Vector Norms, Chebyshev Polynomial | Assignment 99.2 Copy of today's slides |
HY:Ch3.1-2,Ch4.1-2, Workbook pp 135-169, slides in back |
| L8 | Th | Feb 11 | Norms, Symmetrizable iter, Adaptive Chebyshev, Def. of pseudo residual, Notation for normalized Chebyshev polyn., Slides on Chebyshev Accel | Copies of Slides? | Slides from 1990 |
| L9 | Tu | Feb 16 | Vector norms, Conjugate Gradient 2-term formula | Copies of slides? | 1990 slides, Anne's notes + DMY notes |
| L10 | Th | Feb 18 | Conjugate Gradient -- 3-term | 1990 Slides in 3-term CG; HY pp140-141 | |
| L11 | Tu | Feb 23 | DMY: ITPACK 2C; ACE: MODGDP and FORTRAN |
1)ITPACK 2C (TOMs article) 2)"IV.2: Subroutine MODGDP: Use w/ ITPACK 2C (same as WB pp271-276) 3)"FORTRAN FOR ITPACK USERS" by ACE Feb 23, 1999 4)"USING ITPACK 2C on UT Math Suns", by ACE Nov 19, 1998 |
Handouts |
| L12 | Th | Feb 25 | ACE: MODGDP and TOMs article on ITPACK 2C DMY: 15 mins. on Tridiagonal Systems |
"Modified Thomas Method and Block Iterative Methods, Sup 93.5.3 (incl. 2 pages on Block-Jacobi covered later) | handouts |
| L13 | Tu | Mar 02 | Solutions of Tridiagonal Systems |
1)"Solutions of Tridiagonal Systems (Sup 98.3.31) +
extra summary sheet (attached); 2)"Assignment 99.4 on MODGDP" |
Handout |
| L14 | Th | Mar 04 | ACE: More on Line Methods, Block Jacobi; DMY: ADI-- Example and Basic Formula (on handout) ACE: Peaceman-Rachford |
-none- | Slides from 1990 Workbook |
| L15 | Tu | Mar 09 | SOR for Consistently Ordered Matrices | -none- | Slides in workbook pp 607-610 Y-71:Ch 5.1-6; 6.1-3 Also some material in Workbook pp77-?? |
| L16 | Th | Mar 11 | Michel Pal: Multigrid | -none- | Notes and handouts from Anne |
| - | - | - | SPRING BREAK | - | - |
| L17 | Tu | Mar 23 | Multigrid | 2-3 handouts? | Handouts |
| L17 | Tu | Mar 23 | Non-symmetrizable case -- Krylov Space Methods: Idealized Generalized CG, ORTHODIR, ORTHOMIN, ORTHORES | Copy of slides -- Lect 13, 1990 | HY-81: 12.3; Slides (Lect. 13, 1990) |
| L18 | Tu | Mar 30 | IGCG Special Cases | 1)Chen's thesis Ch1-5.2 2) Copies of slides, Lect 14 (WB pp 637-641) 3) Assignment 99.5A: Find error(s) on p 12 of Chen's Thesis |
HY-81: 12.5-6; Slides 14.1-8, Chen's Thesis: Ch 3; |
| L18 | Th | Apr 01 | Conjugate residual method (Z=A^T); GCW (Q = 1/2(A + A^T)); Examples:Convection-Diffusion Eqn (A PR and Jacobi), Complex Chebyshev | Handout 14.2a | Slides 14.9-14.18, Chen's Thesis: Ch 4, HY-81: Ch 12.5-6, 12.2 |
| L19 | Tu | Apr 06 | Lanczos/Bi-conjugate Gradient | Copies of slides -- Lect 15, 1990 | Chen's Thesis, Ch 4, HY-81, Ch 12 |
| L20 | Th | Apr 08 | ORTHORES -> Lanczos; NSPCG |
1) ORTHORES -> ORTHORES/Lanzos (notes by ACE April '99); 2) ITPACK/NSPCG overview (notes by ACE Apr 1999); 3) CNA Report 228 -- Overview of NSPCG 4) Mini Assignment 2 (via e-mail on ELLPACK format) |
Handouts, Chen's thesis |
| L21 | Tu | Apr 13 | NSPCG/ Project descriptions + overview of PIC methods | - none? - | CNA report on NSPCG |
| L22 | Th | Apr 15 | Complex Chebyshev, Lanczos (review) |
1) Complex Chebyshev slide copies (Apr 15, 1999 by ACE), 2) Lect Notes 15.5-15.12 incl. addendums 15.6a-c. |
Handouts, HY-'81, Ch 12 |
| L23 | Tu | Apr 20 | Given's rotations, GMRES overview |
1)Chen's Thesis (handed out earlier), 2)Mini assigment 3 (on board -- Prob 5.1.7 in GVL p209), 3)Sect. on Householder and Given's transformations from GVL Ch 5. |
Handouts, Chen's thesis Ch 5 |
| L22 | Tu | Apr 22 | Dr. Linda Hayes: Finite Elements | - none- | Black board notes |
| L24 | Tu | Apr 27 | More on GMRES | TBD | - |
| L25 | Tu | Apr 29 | Dr. Linda Hayes: Block Methods and ADI | TBD | - |
| L25 | Tu | May 04 | Student presentations/ Course survey? | TBD | - |
| L25 | Tu | May 06 | LAST CLASS -- Student presentation, course survey? | -TBD | - |