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Results tagged with numerical-analysis
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user 683
1
vote
Accepted
$fl(x)=x(1+\delta)$
The idea that this expression is trying to relay is that the nature of the error in floating-point arithmetic is multiplicative rather than additive (which is the case for fixed-point arithmetic). Thi …
- 279k
1
vote
Accepted
Numerical issues in solving linear systems
The $2\times 2$ matrix has determinant close to zero, and so its condition number is very large, causing numerical instability.
The explicit solution of your system is
$$
x=\frac{a}{a^2-b^2}, y=-\fra …
- 279k
13
votes
Accepted
Computing inverse matrix when an element changes
The Sherman-Morrison formula could help:
$$ (A + uv^T)^{-1} = A^{-1} - \frac{A^{-1} uv^T A^{-1}}{1 + v^T A^{-1} u}. $$
Let $u = (a'_{ij}-a_{ij}) e_i$ and $v = e_j$, where $e_i$ is the standard basis c …
- 279k