King Fahd University of Petroleum & Minerals
Department of Mathematical Sciences
MATH 471 - Numerical Analysis I (3-0-3)
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Syllabus
Floating-point, round-off analysis. Solution of linear algebraic systems: Gaussian elimination and LU decomposition, condition of a linear system, error analysis of Gaussian elimination, iterative improvement. Least squares and singular value decomposition. Matrix eigenvalue problems.
Objectives
This course is designed to introduce the students to the numerical Linear algebra problems. Catalogue Description Floating point, round-off analysis. Solution of linear algebraic systems: Gaussian elimination and LU-decomposition, condition of a linear system, error analysis of Gaussian elimination, iterative improvement. Least squares and singular value decomposition. Matrix eigenvalue problems.
Prerequisite:
Math 280, Math
321 or SE 301
Textbook: Numerical Analysis by Burden and Faires, 7th edition (2001).
Grading
Policy:
First
and Second Exam 40%.
Final
35%.
Assignments
10%
Programming
Assignments 15%
|
Week # |
Sections |
Topics |
|
1 |
1.1 |
Review
of some topics Introduction,
|
|
2 |
1.2 |
Startup
with MATLAB Roundoff
Errors |
|
3 |
1.3 |
Roundoff
Errors (cont.) Algorithms
and Convergence |
|
4 |
6.1 6.2 |
Gaussian
Elimination Pivoting
|
|
5 |
6.3 and 6.4 6.5 |
Linear
Algebra and Determinants LU
Factorization |
|
6 |
6.6 |
LDL
Factorization |
|
7 |
6.6 6.7 |
Choleskis
Factorization Programming
|
|
8 |
7.1 7.2 |
Norms Eigenvalues |
|
9 |
7.3 |
Jacobi
and Gauss-seidle methods, SOR |
|
10 |
7.4 7.5 |
Errors CGM |
|
11 |
8.1 |
Approximation |
|
12 |
8.2 |
Polynomials |
|
13 |
9.1 9.2 |
Eigenvalues Power
method |
|
14 |
9.3 |
Householders
method |
|
15 |
9.4 |
QR
method SVD |