Referring to sparse matrices with concentrations of non-zero elements along a combination of diagonals, subdiagonals, and/or superdiagonals.
2
votes
2answers
114 views
Efficient computation of Markov chain transition probability matrix
Consider a continuous Markov chain $X=(X_t)$ on a finite state space and let $Q$ be the (given) transition rate matrix. This matrix is very sparse, with non-zero values on 3 diagonals only (so from ...
4
votes
2answers
534 views
Writing the Poisson equation finite-difference matrix with Neumann boundary conditions
I am interested in solving the Poisson equation using the finite-difference approach. I would like to better understand how to write the matrix equation with Neumann boundary conditions. Would someone ...
3
votes
2answers
255 views
How should I build a 2D 5-point stencil Laplacian matrix in parallel?
I'm making a simple eigenvalue solver with SLEPc, using a 5-point stencil and the finite difference method. I want to be able to assemble the matrix in parallel.
My first thought was just to use ...
6
votes
1answer
482 views
How does LAPACK solve tridiagonal systems and why
In my project I have to solve a couple of tridiagonal matrices at every time step, so it is crucial to have a good solver for those. I did my own implementation, just the classical way to do it ...
2
votes
2answers
165 views
What heuristics can be used to minimize the asymptotic matrix bandwidth of a 5-point Laplacian discretization?
I can see that there are multiple heuristics to acheive a matrix with minimum bandwidth. As heuristics, they can't guarantee an optimal solution in polynomial time (after all, the problem is NP ...
6
votes
4answers
415 views
How to reorder variables to produce a banded matrix of minimum bandwidth?
I'm trying to solve a 2D poisson equation by finite differences. In the process, I obtain a sparse matrix with only 5 variables in each equation, For example, if the variable were U, then the ...
3
votes
2answers
154 views
How to parallelize a banded direct solver?
I have a linear system whose matrix that is diagonally dominant, non-symmetric, but banded. Since the band-radius is 2 (producing only 5 variables per equation), a banded direct solver (gaussian ...
