# Class schedule

*Note*: This schedule is subject to revision during the term.
**Wednesday, September 2**

Introduction to numerical analysis.
**Friday, September 4**

Floating point arithmetics, well-posedness and well conditioning, stability, backward stability.
**Wednesday, September 9**

Gaussian elimination. LU decomposition.
**Friday, September 11**

Gaussian elimination with partial pivoting. Cholesky decomposition.
**Wednesday, September 16**

QR decomposition. Gram-Schmidt process. Householder reflection. Least-squares problems.
**Friday, September 18**

Conditioning and stability revisited. Stability of solving linear systems with QR decomposition. Stability of GEPP.
**Wednesday, September 23** - (*Homework 1 due*)

Fixed point iterations. The Banach fixed point theorem.
**Friday, September 25**

Stationary iterative methods for linear systems. Splitting methods. Jacobi and Gauss-Seidel.
**Wednesday, September 30**

Relaxation schemes.
Richardson.
Nonstationary iterative methods.
Steepest descent.
**Friday, October 2**

Conjugate directions. Conjugate gradients.
**Wednesday, October 7**

Krylov subspaces. Arnoldi. GMRES. Preconditioning.
**Friday, October 9** - (*Homework 2 due*)

Midterm.
**Wednesday, October 14** - (*No class*)

**Friday, October 16** - (*No class*)

**Monday, October 19**

Nonlinear equations in **R**. The Newton-Raphson method. Bisection method.
**Wednesday, October 21**

Secant method. *Regula Falsi*. Round-off error. Conditioning. Stopping criteria.
**Friday, October 23**

Aitken's extrapolation. Nonlinear equations in **R**^{n}. Fixed point iterations. Newton's method.
**Monday, October 26**

Inexact Newton methods. Broyden's method. Forcing global convergence. Continuation method. A glance at nonlinear unconstrained optimization.
**Wednesday, October 28**

Roots of polynomials. Horner's scheme. Deflation. Sturm sequences. Euclid's algorithm.
**Friday, October 30**

Bernoulli iteration. Muller's method. Bairstow's method.
**Wednesday, November 4** - (*Homework 3 due*)

Matrix eigenvalue problems. Using the characteristic polynomial. Hessenberg matrix. Power iterations.
**Friday, November 6**

Inverse, and Rayleigh quotient iterations. Jacobi, QR, and LR iterations. Reduction to Hessenberg form.
**Wednesday, November 11**

Polynomial methods for symmetric tridiagonal eigenvalue problems.
**Friday, November 13**

Subspace iteration. Simultaneous iterations. Basic QR. Francis' Implicit QR method.
**Wednesday, November 18** - (*Homework 4 due*)

Polynomial interpolation. Lagrange coefficients. Newton's polynomials. Divided differences.
**Friday, November 20**

Numerical quadrature. Interpolatory quadrature. Gauss quadrature. Orthogonal polynomials. Least squares approximation.
**Wednesday, November 25**

Uniform approximation. Chebyshev polynomials. Applications to interpolation and the convergence theory of CG.
**Friday, November 27**

Trigonometric polynomials. Fast Fourier transform.
**Wednesday, December 2** - (*Homework 5 due*)

Review.
**Thursday, December 10**

Final exam.