Department of MathematicsThis 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
- 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