Math 561 Syllabus

This is a Qualifying Eligible (QE) course for the Math PhD with regular, graded HW and a comprehensive final exam.

Prerequisites

The equivalent of Math 212 and 221.  Some coding experience with Matlab/Python/C.

Syllabus

Singular Value Decomposition, Principle Component Analysis, QR Factorization, Least Square Problems, Conditioning and Stability, Direct Method for Linear Systems – Gaussian Elimination, Cholesky Factorization, Iterative Methods for Linear Systems – Conjugate Gradients, GMRES, Preconditioning,  Eigenvalue Problem – Power Method, Rayleigh Quotient, Inverse Iteration, QR Algorithms, Newton Method for Nonlinear Equation, Multigrid Method and Fast Fourier Transform.

References

Numerical Linear Algebra, by Lloyd Trefethen and David Bau

References

Matrix Computations, by Gene H. Golub and Charles F. Van Loan Applied Numerical Linear Algebra, by James Demmel Solving Nonlinear Equations with Newton’s Method, by C. T. Kelley