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1500 questions
9
votes
3 answers
Accuracy issues with Arpack in Julia for eigenvalues of smallest magnitude
Following the documentation of Julia's Arpack package (Cf. https://julialinearalgebra.github.io/Arpack.jl/stable/eigs/) I have computed some largest and smallest magnitude eigenvalues of sparse matrices encoded in the required CSC format and noticed…
Stavros Kousidis
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9
votes
4 answers
Hosting site for a small scientific library
For my research work I have been developing a small C++ library aimed at facilitating the communication between C++ computational codes and Octave/Matlab (when the latter is used for post-processing purposes).
I would like release such a library…
Acorbe
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9
votes
2 answers
When is it easy to invert a sparse matrix?
(Crossposted on cstheory.SE)
When is it easy to invert a sparse matrix? Specifically, I'm wondering about the cases in which matrix inversion has similar cost to sparse matrix multiplication, hence much lower cost than full matrix inversion.
If the…
Yaroslav Bulatov
- 2,655
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9
votes
1 answer
Matlab Pde Toolbox: Plot solution on a line or on a submanifold
I'm using the Matlab pde toolbox to solve a certain elliptic equation in 2D.
Solution is fine, although I do need to plot it along a given line, i.e. to cut a planar slice from the 3D mesh representing the solution.
I can't figure out a way that…
Acorbe
- 313
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9
votes
4 answers
Finite-difference software for solving custom equations
Are there any good, easy to use, software for simulating the evolution of systems of generic differential equations? I know there are custom programs for various specific circumstances (such as electrodynamics). But say I have some equations and I…
Tom
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9
votes
4 answers
Checking singularity of a matrix
Suppose that we don't know $n \times n$ matrix $A$ explicitly but we are only able to compute products $Ax$ where $x$ is a column vector with $n$ elements. Is there an algorithm to determine whether $A$ is singular?
tohoyn
- 331
- 1
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9
votes
3 answers
Fastest algorithm to compute the condition number of a large matrix in Matlab/Octave
From the definition of condition number it seems that a matrix inversion is needed to compute it, I'm wondering if for a generic square matrix (or better if symmetric positive definite) is possible to exploit some matrix decomposition to compute the…
linello
- 273
- 3
- 9
9
votes
2 answers
How to remove Rigid Body Motions in Linear Elasticity?
I want to solve $K u = b$ where $K$ is my stiffness matrix. However some constraints may be missing an therefore some rigid body motion may be still present in the system (due to eigenvalue zero). Since I'm using CG for solving the linear system…
Tom
- 465
- 4
- 14
9
votes
1 answer
Increasing computational performance by using 16 bit numbers
I recently found the following article where it was stated that using 16 bit numbers can be used to increase the computational performance of AI applications. According to the article numbers above 16 bit must be scaled to fit into the 16…
vydesaster
- 840
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- 11
9
votes
3 answers
Recommendations for a lightweight/no-install C or C++ based dense linear algebra solver
Most of my programming is one-off research codes in C for my own use. I have never distributed any code to other than close collaborators. I have developed an algorithm that I am publishing in a scientific journal. I want to provide the source code…
jep
- 193
- 2
- 7
9
votes
1 answer
Fast (approximate) evaluation of Chebyshev polynomial
Is there a preferred way how to implement a fast (approximate) evaluation of the Chebyshev interpolation polynomial on uniform grid (given the function values at the Chebyshev nodes)? My problem is that the interpolation becomes slow when the degree…
Thomas Klimpel
- 2,141
- 15
- 35
9
votes
2 answers
Simultaneous maximization of two functions without available derivatives
I have two variables k and t as functions of two other variables p1 and p2. I also know their maximum values. I do not have any analytic expression for this. I want to find the values of k and t which are the closest to their maximum values.
Is…
user1639
9
votes
0 answers
What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?
I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in Economics is when to exercise an expansion…
9
votes
1 answer
Linearized implicit time stepping
Consider the general FD implicit time stepping scheme
$\frac{x_{t+1} - x_t}{\Delta t} = f(x_{t+1})$,
where $x$ is the vector variable of interest and $f$ is some function, generally non-linear.
We can advance from $x_{t}$ to $x_{t+1}$ using…
Patrick
- 455
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9
votes
2 answers
Fastest way to find eigenpairs of a small nonsymmetric matrix on a GPU in shared memory
I have a problem where I need to find all positive (as in the eigenvalue is positive) eigenpairs of a small (usually smaller than 60x60) nonsymmetric matrix. I can stop calculating when the eigenvalue is smaller than a certain threshold. I know that…
Kantoku
- 91
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