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.

• Finite precision arithmetic and error: ill conditioning, numerical stability.
• Solving systems of linear equations: Gaussian elimination, matrix factorization, methods for special matrices, condition of linear equations, error analysis, methods for large sparse systems, nonlinear systems.
• Solving nonlinear equations: bisection, fixed point iteration, Newton's and secant methods, effects of rounding error, Newton's method for systems of equations.
• Overdetermined syetems and least squares: QR factorization, normal equations
• Interpolation and approximation: polynomial interpolation, divided differences, spline interpolation.
• Differentiation and integration: trapezoidal and Simpson's rules, accuracy, extrapolation methods.
• Methods for ordinary differential equations: initial and boundary value problems.
• Basics of parallel computation.