King Fahd University of Petroleum & Minerals

Department of Mathematical Sciences

MATH 471 - HomePage

MATH 471 - Numerical Analysis  I (3-0-3)

 Assignments #1 2,  3,    4, Assignments #2 2, 2,  3,  4, MatlabAss#6 MatlabAss#7 MatlabAss#8

Syllabus

## Catalog 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.

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: or SE 301

Textbook:  Numerical Analysis by Burden and Faires, 7th edition (2001).

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