Tagged Questions
4
votes
2answers
126 views
Computing matrix exponential with PETSc/SLEPc
My question is basically the best way to compute the matrix exponential in parallel. I've got a sequential code written in Python (https://github.com/hadsed/AdiaQC) and I need to extend it to run in a ...
7
votes
1answer
157 views
What algorithm to use for parallel dense matrix inversion on at most 8 cores?
I need to implement parallel dense matrix inversion for a language I am using that appears to not have an existing library for this (specifically IDL using IDL Bridge for message passing). I am ...
2
votes
1answer
61 views
Cholesky Algorithm loop-Carried
I would like to know how to unroll loop-carried dependency inside the cholesky algorithm. What are the techniques that I should know to accomplish this work?
I need to know it because I want to ...
8
votes
2answers
201 views
Diagonalization of Dense Ill Conditioned Matrices
I am trying to diagonalize some dense, ill-conditioned matrices. In machine precision, results are inaccurate (returning negative eigenvalues, eigenvectors do not have the expected symmetries). I ...
5
votes
1answer
92 views
Practical efficacy of parallel back substitution
The fact that the back substitution is not done in parallel is not
important, because it uses a negligible amount of computer time when N
is large, compared to the forward elimination.
This ...
3
votes
2answers
117 views
What mapping strategy should I use when solving many large linear systems of equations?
I am working on a problem that involves solving many (thousands) of distinct linear systems of equations, each with thousands of variables. Let's assume that the size of each matrix is exactly the ...
3
votes
1answer
171 views
Is a checkerboard block decomposition of a matrix useful when solving a linear system with a parallel conjugate gradient method?
According to these lecture notes, a checkerboard block decomposition should exhibit better scalability when applied to parallel matrix-vector multiplication (presumably because of greater cache hit ...
3
votes
1answer
172 views
Problems running a PETSc example in parallel
After configuring and building PETSc, I have successfully been able to run several examples. In particular, I am working with this example. I have been able to run the program using the following ...
2
votes
1answer
179 views
How to solve a problem with structure similar to a finite difference discretization of the 2D Poisson equation, but with non-symetric coefficients?
Recently, I've been asking about methods to solve a finite difference discretization of the 2D Poisson equation (see here and here) of the form:
$$U_{i-1,j} + U_{i+1,j} -4U_{i,j} + U_{i,j-1} + ...
3
votes
2answers
153 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 ...
6
votes
1answer
297 views
How can one parallelize a multigrid method for solving a linear system of equations?
As I understand it, the multigrid method solves a linear system by solving a coarser version of the same problem (there by eliminating low frequency error) then projecting back to the fine grid to ...
5
votes
2answers
192 views
What guidelines should I use when choosing a scalable linear solver?
There are many different linear solvers, some which work best for diagonally dominant matrices, some for symmetric, some for positive definite ones, some for banded matrices, etc... There are direct ...
4
votes
3answers
456 views
Krylov Subspace Methods for Dense Systems
I am currently researching on the viability of using KS methods for solving large dense systems. What I wish to prove (or disprove) is that methods like CG, BiCG and QMR are as good (if not better) ...
