This is a Qualifying Eligible (QE) course for the Math PhD with regular, graded HW and a comprehensive final exam.
The equivalent of Math 212 and 221. Some coding experience with Matlab/Python/C.
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.
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