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Questions tagged [linear-algebra]

Questions on the algorithmic/computational aspects of linear algebra, including the solution of linear systems, least squares problems, eigenproblems, and other such matters.

8
votes
1answer
918 views

How can I compute the Schur complement in PETSc?

How can I compute the Schur complement: $$ S = K_{bb} - K_{ba} K_{aa}^{-1} K_{ab} $$ where $$ K=\begin{pmatrix} K_{aa} & K_{ab} \\ K_{ba} & K_{bb} \end{pmatrix} $$ (in some ordering) is a ...
14
votes
3answers
1k views

Why is my parallel solver slower than my sequential solver?

I was playing around with PETSc and noticed that when I run my program with more than one process via MPI it seems to run even slower! How can I check to see what is going on?
12
votes
3answers
1k views

Efficient tridiagonal matrix algorithm implementation

I am solving a physical problem using implicit numerical scheme. This leads me to solving a linear equation with tridiagonal matrix. I've coded this algorithm from Wikipedia. I wonder if there is an ...
21
votes
2answers
8k views

Libraries for solving sparse linear systems

There are a number of different libraries out there that solve a sparse linear system of equations, however I'm finding it difficult to figure out what the differences are. As far as I can tell there ...
48
votes
4answers
6k views

What guidelines should I follow when choosing a sparse linear system solver?

Sparse linear systems turn up with increasing frequency in applications. One has a lot of routines to choose from for solving these systems. At the highest level, there is a watershed between direct (...
15
votes
1answer
3k views

How can I estimate the condition number of a large sparse matrix using PETSc?

I have a PETSc Mat and would like to estimate its condition number.