Time and Place:
- Preliminaries: floating point arithmetic, round-off errors and stability. Matrix norms and the condition number of a matrix.
- Introduction to numerical solutions for ODE’s:initial value problems, Euler’s method, introduction to multistep methods. Boundary value problems.
- Numerical solution of linear equations: Gauss elimination with pivoting, LU decomposition. Iterative techniques: Jacobi, Gauss-Seidel, conjugate gradient. Least squares approximation.
- Numerical methods for finding eigenvalues: Gershgorin circles. The power method. Stability considerations in Gram-Schmidt: Hausholder reflections and Givens rotations. Hessenberg and tridiagonal forms. QR decomposition and the QR algorithm.