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Numerical Analysis I
Lecturer: Dr M.R. O'Donohoe
No. of lectures: 8
This course is a prerequisite for Numerical Analysis II, Digital Signal Processing (Part II).
Aims
The aims of this course are to provide introductions to floating-point
arithmetic, numerical analysis and numerical software. Current
implementations of floating-point arithmetic will be described. The
basic principles of good numerical techniques will be illustrated by
examples, but it will be shown that the design of a numerical
algorithm is not necessarily straightforward, even for simple
problems. The emphasis of the course will be on principles and
practicalities rather than mathematical analysis.
Lectures
- Floating-point arithmetic.
General description; the numerical analyst's view; overflow and
underflow. [0.6 lectures]
- Errors in numerical methods.
Machine epsilon; error analysis; solving quadratics; convergence;
error testing; rounding error; norms. [1.8 lectures]
- Condition and stability.
Condition of a problem; stability of an algorithm. [0.6 lectures]
- Order of convergence; computational complexity. [0.3 lectures]
- IEEE arithmetic.
The IEEE Floating-point standards. [1 lecture]
- Simple numerical methods.
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. [3 lectures]
- Numerical software.
Portability; languages; the Brown model; implementation
issues for IEEE arithmetic, automatic quadrature, BLAS. [0.7 lectures]
Objectives
At the end of the course students should
- appreciate both the historical significance of numerical
computation and its continued relevance to the solution of
mathematical problems
- understand the advantages and limitations of IEEE arithmetic
- be able to apply a small number of numerical techniques with
an understanding of their underlying principles
- understand the special considerations needed when implementing
floating-point algorithms in re-usable software
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.
Next: Operating System Foundations
Up: Michaelmas Term 2003
Previous: Mathematics for Computation Theory
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Christine Northeast
Thu Sep 4 13:12:26 BST 2003