Numerical Analysis I

Lecturer: Dr M.R. O'Donohoe (mro2@cam.ac.uk)

No. of lectures: 8  

Floating-point arithmetic.

General description; the numerical analyst's view; overflow and underflow.

Errors in numerical methods.

Machine epsilon; error analysis; solving quadratics; convergence; error testing; rounding error; norms.

Condition and stability.

Condition of a problem; stability of an algorithm.

Order of convergence; computational complexity.

IEEE arithmetic. The IEEE Floating-point standards.

Simple numerical methods: differentiation, approximation.

Differentiation; finite differences; splines. Linear and non-linear equations. Gaussian elimination; Choleski factorisation; linear least squares; Newton-Raphson iteration. Integration. Quadrature rules; summation of series.

Numerical software.

Languages; the Brown model; implementation issues for IEEE arithmetic; automatic quadrature; portability; BLAS.

Recommended books:

Conte, S.D. & Boor, C. de (1980). Elementary Numerical Analysis. McGraw-Hill.

Shampine, L.F., Allen, R.C. Jr & Pruess, S. (1997). Fundamentals of Numerical Computing. Wiley.