Course Description

MA 580 explores the theory and practice of numerical algorithms for solving fundamental problems in linear algebra and scientific computing. The course develops techniques for solving systems of equations, performing matrix factorizations, and applying iterative methods — all with a focus on computational efficiency, stability, and accuracy.

Topics Covered

• Floating-point arithmetic and roundoff error
• Direct methods for linear systems (LU, Cholesky, QR)
• Least squares problems (Householder and Givens methods)
• Stationary iterative methods (Jacobi, Gauss-Seidel, SOR)
• Krylov methods: Conjugate Gradient, GMRES
• Condition numbers, convergence theory, error analysis

Learning Outcomes

By the end of the course, students will be able to:

• Choose and implement stable and efficient numerical algorithms
• Analyze convergence and failure of iterative solvers
• Understand trade-offs between accuracy, complexity, and performance
• Develop technical documentation and reproducible numerical results in LaTeX and MATLAB

Textbooks & Resources

All required texts are freely available via NC State Library:

1. Ipsen, I. C. F.
   Numerical Matrix Analysis, SIAM, 2009
   Borrow from NCSU Library

2. Kelley, C. T.
   Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995
   Borrow from NCSU Library

3. Higham, D. J. & Higham, N. J.
   MATLAB Guide (2nd ed.), SIAM, 2005
   Borrow from NCSU Library

4. Some helpful notes from Dr. Moody Chu

Grading Breakdown

• Homework (5 LaTeX-based assignments): 40%
• Two Proctored Tests: 30% (15% each)
• Comprehensive Final Exam: 30%

Tips for Self-Guided Learning

• Use Ipsen for theory and matrix properties
• Use Kelley for algorithmic intuition and exercises
• Use Higham & Higham for MATLAB-driven examples
• Watch Dr. Kelley’s lectures on WolfWare to reinforce methods
• Use MathWorks MATLAB for hands-on experimentation

This page summarizes the Spring 2025 offering. Policies may differ in future semesters.