Algorithm behavior and applicability. Effect of roundoff errors, systems of linear equations and direct methods, least squares via Givens and Householder transformations, stationary and Krylov iterative methods, the conjugate gradient and GMRES methods, convergence of method.

Upon completion, students will be able to:

• Analyze the behavior and applicability of numerical algorithms, considering factors such as stability, accuracy, and efficiency.
• Implement direct methods for solving systems of linear equations, including techniques like Gaussian elimination with partial pivoting.
• Apply least squares methods using Givens and Householder transformations to approximate solutions for overdetermined systems.
• Evaluate the effectiveness of stationary and Krylov iterative methods, including the conjugate gradient and GMRES, in solving linear systems.
• Assess the convergence properties of numerical methods and understand their limitations.

Grade Basis: L
Credit hours: 3.0
Lecture hours: 3.0