Numerical Computation Preliminary Exam
The numerical computation is usually a one-week take home examination
consisting of a few questions requiring thoughtful
and creative answers with access to any written sources allowed.
Familiarity with the content of CSCI 5606 is assumed, including the following topics.
Useful references are "Numerical Analysis: Mathematics of Scientific Computing"
by Kincaid and Cheney and "Scientific Computing" by Michael Heath.
- Finite precision arithmetic and error: ill conditioning,
- Solving systems of linear equations:
Gaussian elimination, matrix factorization, methods
for special matrices,
condition of linear equations,
error analysis, methods for large sparse systems,
- Solving nonlinear equations:
bisection, fixed point iteration, Newton's and secant
methods, effects of rounding error,
Newton's method for systems
- Overdetermined syetems and least squares: QR factorization, normal equations
- Interpolation and approximation:
polynomial interpolation, divided differences,
- Differentiation and integration:
trapezoidal and Simpson's rules, accuracy,
- Methods for ordinary differential equations:
initial and boundary value problems.
- Basics of parallel computation.