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1. Error handling in linear algebra
1.1 Problem position
The problem is essentially this: given a linear operator u, if a vector x is known to an accuracy ε, what accuracy can we expect for the vector u (x)? The notion of precision of a vector will be detailed by introducing norms. We will also study the inverse problem, relating to u -1 , which is essentially that of determining the precision of a solution to a linear equation.
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Error handling in linear algebra
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The actual implementation of the methods described above requires highly precise computer techniques which the size of this article does not allow us to cover. In any case, "off-the-shelf" programs are not always well-suited to real-life situations, which may require prior simplifications, estimates of tolerable errors, etc.
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