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1. Solving non-linear equations and systems
Let f be a continuous application of in itself. The problem we'll be looking at in this paragraph is that of finding x such that f (x ) = 0. We then say that x is a root of f. Another, completely equivalent way of posing the same problem is to find x such that x = F (x ). We then say that x is a fixed point of F. In the following, when we use the letter f (in a theorem or algorithm), this implicitly means that the problem to be solved is put in the form f (x ) = 0. When we use the letter F, it means that our problem is written in the form x = F (x ). These two formulations are equivalent because, if it's in the form f (x ) = 0, we also have x = x + af (x ) = F (x ) with any a 1 0. Conversely, if x = F (x...
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Solving non-linear equations and systems
Solving systems of linear equations
Bibliographies
References
Publications on numerical analysis
(list in alphabetical order, not exhaustive)
Advances in Computational Mathematics
Applied Numerical Mathematics
BIT Numerical Mathematics
Computer Aided Geometric Design
Constructive Approximation
Journal of Approximation Theory
...
Calculation software
(non-exhaustive list)
The best known is MATLAB http://www.mathworks.fr/
A guide to available calculation software can be found at : http://gams.nist.gov/
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