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MATH 6370 Section 10583
Fall 2007
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December 4, 2007
- Your 3rd exam grades have been sent to you by email. You should receive your final letter grade from UH.
- If you want to see/get your copies, please wait until the start of next semester.
- Answers Exam 3: [pdf]
November 27, 2007
- Material for Exam 3 (Monday December 3, 2007)
- Course notes.
- GMRES algorithm (8.7.2)
- BiCG (8.7.4)
- Basic facts on eigenvalues (6.1) and normal forms (6.2,6.3,6.4)
- Methods for computing eigenvalues (6.6.1,6.6.3,6.6.4)
- Estimation of eigenvalues (6.9)
- Related homework problems (only the ones proposed in class-dismmis the additional problems we have not discusssed for time
reasons).
October 24, 2007
- Material for Exam 2 (Monday November 5, 2007)
- Course notes.
- Data Fitting, Least Squares and Pseudo-inverse (chap 4.8)
- Iterative methods (8.0, 8.1)
- Convergence results (8.2)
- relaxation methods (8.3)
- Block Iterative methods (8.5)
- ADI method (8.6)
- Conjugate gradient algorithm (8.7.1)
- GMRES algorithm (8.7.2)
- Related homework problems.
October 22, 2007
Web References for articles/papers
October 18, 2007
- Demonstration hand out in class :
[pdf]
- A reference about CG method (for your information) :
[pdf]
- The past papers to read have been posted below.
September 21, 2007
- Erratum: The algorithm given in the answers of the additional
exercise 4 (chapter 4) is the Cholesky decomposition algorithm and not the
Gaus elimination. This erratum had not influence on the grading of your homework.
September 19, 2007
- Material for Exam 1
- Course notes, including introduction and definition of norms, matrices,
etc.
- Gaussian elimination and LR decomposition (chap 4.1)
- Gauss-Jordan Algorithm (4.2)
- Cholesky decomposition (4.3)
- Error bounds (4.4)
- Orthogonalization techniques (4.7)
- Data fitting (only up to today's class)
- Homework exercises (up to next Monday)
September 17, 2007
- Change of schedule!!!
The second exam will take place on Monday November 5, 2007 (instead of Wednesday
November 7).
September 12, 2007
NO CLASS TODAY (WEATHER REASONS).
HW TO TURN IN ON NEXT MONDAY. NEW HW AND READINGS FOR NEXT MONDAY: SEE BELOW.
August 27, 2007
- No class on Wednesday September 5. (During the
week Sep 3 - 7, office hours by email only).
SYLLABUS/HOMEWORKS/ETC.
- Office Hours : MT 2:00-3:00 PM or by
appointment.
- Syllabus :
[pdf]
- Tentative material :
[pdf]
- Reading List :
[pdf]
- Homework Chapter 6 (eigenvalues) :
[pdf]
- Homework Chapter 8 (indirect methods) :
[pdf]
- Homework Chapter 4 (direct methods) :
[pdf]
- Homework Chapter 1 (error analysis) :
[pdf]
ASSIGNEMENTS: (UPDATED REGULARLY)
- Due Nov 28 : (OPTIONAL - IMPROVE YOUR GRADE)
- Read N. Trefethen, future of Scientific Computing
- Exercises chapter 6 : 14 / 22 (a)
- Additional exercises chapter 6 : 1 (!typo)
- Answers : [pdf]
- Due Nov 21 : (OPTIONAL - IMPROVE YOUR GRADE)
- Read A. Meijering, H. A. Van Der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a sym
metric M-matrix (1977)
- Additional exercises chapter 8 : 8 / 9
- Exercises chapter 6 : 1 / 4 (only eigenvalues and characteristic
polynomial) / 10
- Answers : [pdf]
- Due Nov 12 :
- Read Saad, Schultz, GMRES: A generalized minimal residual algorithm for
solving nonsymmetric linear systems (1986)
- Exercises chapter 8 : 16(a)(b)
- Additional exercises chapter 8 : 7 / 11
- Answers : [pdf]
- Due Oct 29 :
- Read Concus, Golub, O'Leary, A generalized CG method for the numerical
solution of elliptic partial differential equations (1976)
- Exercises chapter 8 : 10(a)
- Additional exercises chapter 8 : 2 / 5 (end) / 13
- Answers : [pdf]
- Due Oct 22 :
- Read Hestenes, Stiefel, Methods of conjugate gradients for solving
linear systems (1952)
- Exercises chapter 8 : 8(a)(b)
- Additional exercises chapter 8 : 4 / 5(a) / 12
- Answers : [pdf]
- Due Oct 15 :
- Complete report on first paper.
- Exercises chapter 8 : 1
- Additional exercises chapter 8 : 1 / 3
- Answers : [pdf]
- Due Oct 8 :
- Read Golub, Kahan, Calculating the singular values and pseudo-inverse
of a matrix (1965)
- Exercises chapter 4 : 14 / 15
- Additional Exercises chapter 4 : 10
- Answers : [pdf]
- Due Sep 24 (extended to Oct 1 ):
- Read P. E. Gill, G. H. Golub, W. Murray and M. A. Sanders, Methods for
modifying matrix factorizations (1974)
- Read G. Golub, Numerical methods for solving linear least squares
problems (1965)
- Exercises chapter 1 : 1 / 3
- Exercises chapter 4 : 3 / 6
- Answers : [pdf]
- Due Sep 17 :
- Read A. S. Householder, Unitary triangularization of a nonsymmetric
matrix (1958)
- Additional Exercises chapter 4 : 7 / 8
- Answers : [pdf]
- Due Sep 10 (extended to Sep 17 !) :
- Read V. Strassen, Gaussian elimination is not optimal (1969)
- Read J.H. Wilkinson, Error analysis of direct methods of matrix
inversion (1961)
- Exercises chapter 4 : 8 / 11 / 13
- Additional Exercises chapter 4 : 3 / 4 / 6 / 11
- Answers : [pdf]
- Due Aug 27 :
- Read L. N. Trefethen, Definition of Numerical Analysis, (1992)
- Exercises chapter 4 : 1
- Additional Exercises chapter 4 : 1 / 2 / 5
- Answers : [pdf]
DOCUMENTS:
- L. N. Trefethen, Definition of Numerical Analysis, (1992):
[pdf]
- V. Strassen, Gaussian elimination is not optimal (1969), 354--356.
[pdf]
- J.H. Wilkinson, Error analysis of direct methods of matrix inversion (1961):
[pdf]
- P. E. Gill, G. H. Golub, W. Murray and M. A. Sanders, Methods for modifying matrix factorizations (1974):
[pdf]
- G. Golub, Numerical methods for solving linear least squares problems (1965):
[pdf]
- G. Golub and W. Kahan, Calculating the singular values and pseudo-inverse of a matrix (1965):
[pdf]
- A. S. Householder, Unitary triangularization of a nonsymmetric matrix (1958):
[pdf]
- M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems (1952):
[pdf]
- L. N. Trefethen, Future of Scientific Computing, (1998):
[pdf] [ps]
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