# Fastest linear solver for sparse positive semidefinite, striclty diagonally dominant matrix

What is the state of the art for fastest linear solver for sparse, positive semi definite and strictly diagonally dominant matrix with N varies from ~700 to ~3000, and about a 1/16 of the matrix is non zero values?
(an existing library is preferred over an algorithm - C/C++).

Thanks.

• These are small enough that the thread-parallelized dense solvers like the LAPACK routines in the MKL are probably the fastest choice. What have you been using? Octave can solve a $3000 \times 3000$ dense random linear system on my laptop, serially in less than half a second. What's your workload look like? Do you need to solve millions of these? – Bill Barth Sep 9 '14 at 13:00
• I'm a bit confused by the Question statement. If a square matrix is strictly diagonally dominant, then it is nonsingular. Consequently positive semi-definite would become positive definite. Am I misunderstanding the situation? – hardmath Sep 10 '14 at 1:51
• I don't have enough rep to vote for the dupe, but scicomp.stackexchange.com/questions/14497/… asks about graph Laplacian matrices and there's a simple reduction from SDD systems to graph Laplacians. – tmyklebu Sep 10 '14 at 2:51