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Results tagged with finite-difference
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user 4405
Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.
4
votes
Accepted
Solve eigenvalue problem using finite differences without vectorization
For sure it is possible with iterative methods, because you can apply your operator $u\mapsto Au$ cheaply while keeping $u$ in "matrix form". It is simply a double nested for cycle. Check out ARPACK, …
- 12.5k
5
votes
Howo to implement complex step derivative for complex functions?
I'm afraid the method only works to compute derivatives of real-valued functions (of which you happen to have an implementation that also works on complex values).
- 12.5k
3
votes
Factorize laplacian in terms of first derivative matrix
@lightxbulb's answer gives the correct factorization already, but since you mention failed attempts with the Cholesky factorization, let me describe a method to discover the factorization numerically, …
- 12.5k
1
vote
How to reorder variables to produce a banded matrix of minimum bandwidth?
While all the present answers are valid solutions to the practical problem, technically the answer to the question in your title (how to reorder variable to minimize bandwidth) is "it's an NP-complete …
- 12.5k
6
votes
Eigenvectors of Laplacian
They're on Wikipedia, for instance, in a page with the slightly unclear name of "Eigenvalues and eigenvectors of the second derivative".
- 12.5k