The numerical tag has no wiki summary.
3
votes
0answers
29 views
Why do I get “estimated error” -1.#IND when doing BICGSTAB linear solver using ILUT perconditioner in eigen
I'm using Eigen (a C++ library for numerical linear algebra) to solve a linear equation with the the bi-conjugate gradient BICGSTAB algorithm with Incomplete LU preconditioner. However, the result ...
4
votes
1answer
49 views
Solving Coupled ODE eigenvalue problem
I've been trying to find some resources that would help me figure out how to numerically solve a coupled system of ODEs which is also an eigenvalue problem.
The system is something like:
$ \tag{1} ...
3
votes
1answer
38 views
Closed form for singular values of 2D Laplacian?
Does anyone know where to find an analytic form for the singular values of the finite-difference approximation to the 2D Laplacian, expressed in matrix form for a square grid? This would be for the ...
8
votes
2answers
169 views
Astoundingly large difference when evaulating trigonometric identity with NumPy
According to Wolfram Alpha and the Sage computer algebra system, the following identity holds:
$$
\cos\left(\arctan\left(\frac{l_1-l_2}{d}\right)\right) = \frac{1}{\sqrt{1 + \frac{(l_1-l_2)^2}{d^2}}}
...
6
votes
4answers
166 views
Relevance of fixed-point and arbitrary precision computations
I see very few non-floating point computing libraries/packages around. Given the various inaccuracies of floating point representation, the question arises why there aren't at least some fields where ...
4
votes
2answers
107 views
Imposing invertibility on a Matrix
I have a symmetric positive semidefinite covariance matrix $A$, which is approximately computed as the output of a quadratic regression. I then need to invert $A$, but often it is close to singular. ...
6
votes
3answers
102 views
Regression testing of chaotic numerical models
When we have a numerical model that represents a real physical system, and that exhibits chaos (e.g. fluid dynamics models, climate models), how can we know that the model is performing as it should? ...
4
votes
1answer
78 views
Bounded Variation Spaces
Could someone explain me (roughly) the interest of Bounded Variation (BV) Spaces for PDEs ?
Is there any numerical application of those space to real problems or is it just a theoretic way to ...
10
votes
1answer
159 views
Catastrophic cancellation in logsum
I'm trying to implement the following function in double-precision floating point with low relative error:
$$\mathrm{logsum}(x,y) = \log(\exp(x) + \exp(y))$$
This is used extensively in statistical ...
28
votes
4answers
629 views
Scientific standards for numerical errors
In my field of research the specification of experimental errors is commonly accepted and publications which fail to provide them are highly criticized. At the same time I often find that results of ...
