CME 302 Numerical Linear Algebra 2023

Weekly schedule Fall 2023 §

1. Introduction to the class; Linear Algebra boot camp
2. Linear algebra boot camp
3. LU factorization, floating point arithmetic, stability, pivoting
4. Cholesky factorization, QR factorization
5. QR factorization and least-squares, normal equation, QR, SVD, eigenvalue computation
6. Eigenvalue computation, power iteration, orthogonal iteration, QR iteration, upper Hessenberg form, QR iteration with shift
7. Iterative methods for eigenvalue computation, Krylov subspace, Lanczos, Arnoldi
8. Classical iterative methods, Jacobi, Gauss-Seidel, SOR
9. Iterative methods for solving sparse systems, Krylov methods, Conjugate Gradients
10. GMRES, Preconditioning, Preconditioned Conjugate Gradients

Class Notes 2023 §

• First lecture
• Bootcamp
• Solving linear systems
• QR factorization and least-squares
• Computing eigenvalues
• Iterative methods for eigenvalue computation
• Classical iterative methods to solve sparse linear systems
• Krylov iterative methods to solve sparse linear systems

Book: Numerical Linear Algebra with Julia, Darve and Wootters