Math 1080: Numerical Linear Algebra Spring 2008
Instructor: David Swigon
Office: Thackeray 519, 412-624-4689, swigon@pitt.edu
Lectures: MWF 11:00-11:50am, Thackeray 627
Office Hours: MW 1:00-3:00pm, Thackeray 519, or by appointment.
Course Web Page: (check frequently for changes and updates) http://www.math.pitt.edu/~swigon/math1080.html
Course Description
The course M1080 gives an introduction to the basic areas of numerical linear algebra. The course will cover the development and analysis of algorithms that are used in the solution of linear algebraic equations, algebraic eigenvalue problems and linear least-square minimization problems.
Prerequisites
Basic knowledge of matrix theory and linear algebra (one of MATH 0250, MATH 0280, or MATH 1180) plus knowledge of computer programming (one of CS 0002, CS 0007, CS 0401, CS 0132) is expected.
Textbook
L. N. Trefethen
& D. Bau III, Numerical Linear Algebra,
SIAM, 1997.
ISBN 0898713617
Grading Scheme
Homework assignments: 30%
Two midterm exams: 20% + 20%
Final exam: 30%
Schedule
The precise schedule and a list of homework problems will be given out in advance and posted on the web. Homework is due in the beginning of a class one week after it was assigned. You may work with other students on homework but do not submit solutions that are identical copies of each other as such will be discarded.
Programming
Many assignments will require computer programming. You are expected to be proficient in at least one computer language, such as Matlab, Fortran, C, Basic, etc. to such an extent that you can write a numerical subroutine, debug it, run it and print out the output. I personally recommend Matlab as it makes manipulation of matrices easy and requires the least coding overhead. I can provide introduction to programming in Matlab but there will be no scheduled computer lab sessions.
You can use any of the University computing labs to work on your assignments.
Matlab resources
Matlab Primer of Professor Sigmon of the University of Florida: http://www.math.pitt.edu/~swigon/Matlab/primer.pdf
Matlab documentation: http://www.mathworks.com/access/helpdesk/help/techdoc/matlab.html
Policy
Attendance is expected. No late homework will be accepted and there will be no make up exams.
Note
This is a course in applied mathematics and hence emphasis will be placed on practical usage of methods and algorithms. Other texts on numerical linear algebra include:
C. G. Cullen, An Introduction to Numerical Linear Algebra, (out of print)
C. F. van Loan, Introduction to Scientific Computing
G. Golub and C. van Loan, Matrix Computation
G. Strang, Linear Algebra and Its Applications
Syllabus
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Date |
Reading |
Topics |
Homework Assigned |
Notes |
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Jan 7 |
I.1-2 pp. 3-16 |
Matrix Multiplication, Orthogonality, Norms |
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Jan 9 |
II.6 pp. 41-47 |
Projectors |
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Jan 11 |
II.7 pp. 48-52 |
QR factorization |
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Jan 14 |
II.7
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QR factorization (cont’d) |
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Jan 16 |
II.8-9 pp. 56-68 |
Gram-Schmidt Orthogonalization |
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Jan 18 |
II.8-9 pp. 56-68 |
Gram-Schmidt Orthogonalization |
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Jan 21 |
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No Class |
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Jan 23 |
II.8-9 pp. 56-68 |
Gram-Schmidt Orthogonalization |
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Jan 25 |
II.10
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Householder Triangularization |
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Jan 28 |
II.11 |
Householder Triangularization (cont’d) |
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Jan 30 |
II.11 |
Householder Triangularization (cont’d) |
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Feb 1 |
II.11 |
Applications of QR factorization |
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Feb 4 |
Review |
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Feb 6 |
Midterm Exam I |
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Feb 8 |
III.12 pp.89-96 |
Conditioning |
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Feb 11 |
III.13 pp.97-101 |
Floating point arithmetic |
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Feb 13 |
III.14 pp.102-107 |
Stability |
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Feb 15 |
III.14 pp.108-113 |
Stability (contd.) |
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Feb 18 |
III.16 pp.114-120 |
Stability of Householder triangularization |
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Feb 20 |
IV.20 pp.147-154 |
Gaussian Elimination |
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Feb 22 |
IV.20 pp.147-154 |
Gaussian Elimination (cont’d) |
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Feb 25 |
IV.21 pp.155-162 |
Pivoting |
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Feb 27 |
IV.21 pp.155-162 |
Pivoting (cont’d) |
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Feb 29 |
IV.22 pp.163-171 |
Stability of Gaussian Elimination |
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Mar 3 |
IV.23 pp.172-178 |
Cholesky Factorization |
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Mar 5 |
Review |
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Mar 7 |
Midterm Exam II Covers Lectures of Feb 8 – Mar 3 |
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Mar 10-14 |
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Spring Break – No Classes |
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Mar 17 |
V.24 pp.181-189 |
Eigenvalue Problems |
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Mar 19 |
V.24 pp.181-189 |
Eigenvalue Problems (cont’d) |
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Mar 21 |
V.24 pp.181-189 |
Eigenvalue Problems (cont’d) |
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Mar 24 |
V.25 pp. 190-195 |
Overview of Eigenvalue Algorithms |
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Mar 26 |
V.26 pp.196-201 |
Reduction to Hessenberg Form |
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Mar 28 |
V.27 pp.202-210 |
Rayleigh Quotient, Inverse iteration |
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Mar 31 |
V.27 pp.202-210 |
Rayleigh Quotient, Inverse iteration (cont’d) |
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Apr 2 |
V.28 pp.211-218 |
QR Algorithm |
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Apr 4 |
V.28 pp.211-218 |
QR Algorithm (cont’d) |
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Apr 7 |
V.29 pp.219-223 |
QR Algorithm with shifts |
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Apr 9 |
I.4 pp.25-31 |
Singular Value Decomposition |
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Apr 11 |
I.5 pp.32-37 |
More on the SVD |
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Apr 14 |
V.31 pp.234-240 |
Computing the SVD |
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Apr 16 |
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Review |
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Apr 18 |
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Q & A |
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Apr 22
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FINAL EXAM 8-9:50am Thack 627 |
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