CS 5223

Numerical Analysis: Linear and Nonlinear Problems

Course Description

Course information provided by the 2026-2027 Catalog.

Introduction to the fundamentals of numerical linear algebra: direct and iterative methods for linear systems, eigenvalue problems, singular value decomposition. In the second half of the course, the above are used to build iterative methods for nonlinear systems and for multivariate optimization. Strong emphasis is placed on understanding the advantages, disadvantages, and limits of applicability for all the covered techniques. Computer programming is required to test the theoretical concepts throughout the course.

Prerequisites background equivalent to: MATH 2210 or MATH 2940, knowledge of programming, CS 3220 or CS 4210/MATH 4250 or permission of instructor.

Last 4 Terms Offered 2026SP, 2025SP, 2024SP, 2023SP

Learning Outcomes

• Analyze sources of error in numerical algorithms and reason about problem stability and how it influences the accuracy of numerical computations.
• Choose appropriate numerical algorithms to solve linear algebra problems (linear systems, least squares problems, and eigenvalue problems), taking into account problem structure.
• Formulate nonlinear equations and constrained and unconstrained optimization problem for solution on a computer.
• Analyze the local convergence of nonlinear solver algorithms.
• Reason about global convergence of nonlinear solver algorithms.
• Use numerical methods to solve problems of practical interest from data science, machine learning, and engineering.

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