CSC 428 - Introduction to Numerical Analysis II

Catalog Description:
Computational procedures including direct and iterative solution of linear and nonlinear equations, matrices and eigenvalue calculations, function approximation by least squares, smoothing functions, and minimax approximations.
Contact Hours:

• Lecture: 3 hours

Prerequisites: [MA305 or MA405] and [CSC111 or CSC112 or CSC113 or CS
Co-requisites: None
Restrictions: None
Coordinator:
Textbook: Numerical Analysis

Course Outcomes:
 By the end of this course students will be introduced to the following:

1. Motivate students to dare their creativity.
2. Introduce students to modern world applications through computer-aided calculation, which in addition to advancing knowledge, might lead to higher level of interest in the computational mathematics.

Topics:

• Review of Linear Algebra
• Norms
• Triangular Systems
• LU Decomposition
• Conditioning and Error Analysis
• QR Decomposition
• Householder Transformation
• Least Squares Models
• Least Squares via QR Decomposition
• Geometric Meaning of Least Squares Solution
• Nonlinear Least Squares Problems
• Singular Value Decomposition
• Generalized Inverse and SVD
• Eigenvalue Problems
• Power Methods
• Inverse Power Methods
• QR Algorithm
• Shifted QR Algorithm
• Generalize Eigenvalue Problems
• Matrix Polynomials
• Error Refinement
• Iterative Methods in General
• Stationary Iteration
• Convergence Theory
• Polynomial Accleration
• Krylov Methods in General

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