: extension of iterative concepts to nonlinear problems using fixed-point iterations, Newton’s method, and quasi-Newton variants like Broyden’s method.
Numerical Methods for Unconstrained Optimization and Nonlinear Equations by Dennis and Schnabel. Matrix Computations by Golub and Van Loan. math 6644
Familiarity with Numerical Linear Algebra (MATH 6643) is strongly recommended but not always required depending on the instructor. : extension of iterative concepts to nonlinear problems
The course is cross-listed as CSE 6644 and serves as an introduction to state-of-the-art iterative algorithms. While direct methods (like LU decomposition) are standard for smaller systems, iterative methods are essential for solving the massive, sparse systems generated by the discretization of differential equations, where direct methods become computationally prohibitive. Core Syllabus Topics math 6644
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