| SUMMARY: |
Lloyd N. Trefethen [40] proposed the following definition of Numerical Analysis:
Numerical Analysis is the study of algorithms for the problems of continuous mathematics.
The keyword here is that of algorithms. Although many papers do not highlight this aspect, the center of numerical analysis is devising and analyzing numerical; algorithms to solve a certain class of problems.
These are the problems of continuous mathematics. “Continuous” means here that real and complex variables are involved; its opposite is discrete. Shortly, one could say that Numerical analysis is continuous algorithmics, as opposed to classical algorithmics, that is discrete algorithmics.
It is clear that since real and complex numbers cannot be represented exactly on computers, they must be approximated using a finite representation. This is where the rounding errors come in and it is clear that their study is one of the important goals of Numerical Analysis. There werw and there exist yet many opinion stating that it is the most important. An argument that supports this idea, excepting the ubiquity of error is given by methods for the solution of linear algebraic syste, such as Gaussian elimination. [...]
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