Course materials:
Syllabus: The course syllabus is found here.
T 01/17 Lecture: Lecture Note 1: ln01.pdf. Preliminaries.
Last updated: 02/05/2017
- Page 6, above Eq.(4.4).
Add a footnote to the equivalence of two norms.
- Page 8, Exercise 3.
Add a clarification of only considering diagonalizable matrices.
Homework 1 due 01/26/2017 Thursday by the end of the class.
T 01/24 Lecture: Lecture Note 2: ln02.pdf. Gaussian elimination, LU decomposition,
and roundoff error analysis.
Last updated: 02/05/2017
- Page 2, below Eq.(1.5).
Add clarification of how L is computed.
- Page 5, at the end of Section 2.
The comment on the rank of A is revised.
- Page 12, Exercise 1.
The two sub-solvers are revised.
Homework 2 due 02/02/2017 Thursday by the end of the class.
T 01/31 Lecture: Lecture Note 3: ln03.pdf. Iterative methods.
Last updated: 02/07/2017
- Page 5, the proof of theorem 3.1 is revised.
- Page 7, the hints of the first two exercises revised.
Homework 3 due 02/09/2017 Thursday by the end of the class.
T 02/02 Lecture: Lecture Note 4: ln04.pdf. The conjugate gradient method.
Last updated: 02/17/2017
- Page 7, a convergence estimate is added.
- Page 1, alpha^2 is added to the big-O term.
T 02/07 Lecture: Lecture Note 5: ln05.pdf. The minimum-residual Krylov methods.
Last updated: 02/17/2017
- Page 1, revised the footnote.
Homework 4 due 02/16/2017 Thursday by the end of the class.
This homework contains exercises in both Lecture 4 and Lecture 5.
TR 02/09 Lecture: Lecture Note 6: ln06.pdf. Generalizing the conjugate gradient method.
T 02/14 Lecture: Lecture Note 7: ln07.pdf. BICGSTAB.
Last updated: 02/19/2017
- Added the computational assignment.
Computational Assignment 1 due 03/09/2017 Thursday by the end of
the class.
Data files:
1) Symmetric problem:
mat_sym_A.txt
mat_sym_b.txt
mat_sym_M.txt
2) Unsymmetric problem:
mat_unsym_A.txt
mat_unsym_b.txt
mat_unsym_M.txt
You could use any programming language you like, but Matlab, C, or
C++ are highly suggested.
A full submission include a brief report including how to build and run
your program, as well as plotting convergence results (the residual
plot).
TR 02/16 Lecture: Lecture Note 8: ln08.pdf. Introduction to least squares problems.
Last updated: 02/19/2017
- Added an appendix showing that col(A^tA) = col(A^t).
T 02/21 Lecture: Lecture Note 9: ln09.pdf. Orthogonal reduction with Givens rotation.
T 02/28 Lecture: Midterm 1 Review.
TR 03/02 Lecture: Midterm 1.
T 03/07 Lecture: Lecture Note 10: ln10.pdf. QR decomposition with Householder
transformations.
TR 03/09 Lecture: Lecture Note 11: ln11.pdf. GMRES revisited using Householder
transformations for orthogonalization and Givens rotations for
the least squares solve of Hessenberg matrices.
Homework 5 due 03/23/2017 Thursday by the end of the class.
T 03/14 Lecture: Spring Break.
TR 03/16 Lecture: Spring Break.
T 03/21 Lecture: Lecture Note 12: ln12.pdf. Introduction to the eigenvalue problem.
T 03/28 Lecture: Lecture Note 13: ln13.pdf. Jacobi algorithm for symmetric matrices.
Computational Assignment 2: See the end of lecture 11.
Target: Implement GMRES and compare the performance with
CGS and BICGSTAB for the non-symmetric problem before.
A full report is required in submission.
Due: 04/06/2017 Thursday by the end of the class.
T 04/04 Lecture: Lecture Note 14: ln14.pdf. The QR method for general matrices.
Last updated: 04/12/2017
- Added the last section in generalized eigenvalue problem.
Homework 6: Exercises of Lecture Note 12.
Due 04/13/2017 Thursday by the end of the class.
T 04/11 Lecture: Lecture Note 15: ln15.pdf. The singular value decomposition.
