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General introduction covering the course structure and context.
Subtitled ``Why computers are bad at maths'', this lecture will present a
detailed investigation of how mathematical concepts such as number and
addition are compromised when we use computers to implement them. This will
examine some of the possible consequences of finite machine precision, and how
such problems may be detected and avoided.
This practical session draws on the material of the previous lecture to
provide a number of realistic test cases where machine mathematics fails, and
how this failure can be overcome.
An overview of some of the major numerical algorithms used to solve various
classes of mathematical problem, and an introduction to some of the most
important numerical libraries that implement those algorithms. This will
include BLAS, (Sca)LAPACK & PETSc.
The Fastest Fourier Transform In The West (FFTW)
is perhaps the best example of a self-optimizing library currently availiable.
This lecture will introduce the concepts and algorithms that allow this
library to combine portability with power & efficiency.
A guest lecture by Prof. Carlos Frenk (University of Durham).
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