# Numerical Analysis II

## 782

*Direct and iterative methods for solving systems of linear equations. Numerical solution of partial differential equations. Numerical determination of eigenvectors and eigenvalues. Solution of nonlinear equations.*

*Numerical Linear Algebra*, Trefethen and Bau III, SIAM, 1997.

MATH 781 or instructor's permission.

This is a sequel of MATH 781 concentrating on numerical linear algebra and optimization. One or two topics will be selected from each of the following units.

- Matrix factorizations for linear equations and least squares. Krylov subspace methods for linear equations and least squares.
- Error analysis and conditioning for linear equations and least squares.
- Unconstrained optimization in several variables including Newton and quasi-Newton methods with line search.
- Methods for the algebraic eigenvalue problem possibly including Jacobi and QR iterations, Krylov subspace methods, and divide & conquer.
- Methods for partial differential equations.
- An additional unit suggested by and of special interest to the class.