Math — 6644

The primary goal of MATH 6644 is to provide students with a deep understanding of the mathematical foundations and practical implementations of iterative solvers. Unlike direct solvers (like Gaussian elimination), iterative methods are essential when dealing with "sparse" matrices—those where most entries are zero—common in the discretization of partial differential equations (PDEs). Key learning outcomes include:

Assessing the efficiency and parallelization potential of different algorithms. Key Topics Covered math 6644

Techniques like Broyden’s method for when calculating a full Jacobian is too expensive. The primary goal of MATH 6644 is to

Foundational techniques such as Jacobi , Gauss-Seidel , and Successive Over-Relaxation (SOR) . Key Topics Covered Techniques like Broyden’s method for

In-depth study of Newton’s Method , including its local convergence properties and the Kantorovich theory .

Choosing the right numerical method based on system properties (e.g., symmetry, definiteness).

Modern, high-performance methods like the Conjugate Gradient (CG) method, GMRES (Generalized Minimal Residual), and BiCG .