Math 578 > Final exam

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

MATH 578: Numerical Analysis 1 Fall 2009