# Final exam

- The final exam is scheduled on Thursday December 10, at 9am
- You are allowed to bring a (double sided) sheet of hand-written notes
- Posted practice questions for the final on WebCT

**Study topics:**
- Gaussian elimination, LU, pivoting, Cholesky
- QR, Gram-Schmidt, Householder, least-squares problems
- Conditioning and stability
- The Banach fixed point theorem, fixed point iterations
- Linear equations: splitting scheme, Jacobi, Gauss-Seidel, relaxation scheme, Richardson, steepest descent, CG, GMRES
- Nonlinear equations: bisection, Newton-Raphson and Newton, secant and Broyden, false position, Aitken's extrapolation
- Polynomial equations: Horner's scheme, deflation, Sturm sequence, Euclid's algorithm, Bernoulli, Muller, Bairstow
- Eigenproblems: Hessenberg form, Sturm sequence for symmetric tridiagonal matrices, deflation
- Power, inverse, Rayleigh quotient, Jacobi, basic QR iterations
- Polynomial interpolation, Lagrangian and Newtonian approaches
- Interpolatory quadrature, Gauss quadrature, orthogonal polynomials, least squares approximation
- Chebyshev's theorem, Chebyshev polynomials, applications to interpolation and the convergence theory of CG