# Special method for finding eigenvalues of a large sparse symmetric matrix?

**URL:** https://discourse.julialang.org/t/special-method-for-finding-eigenvalues-of-a-large-sparse-symmetric-matrix/9621
**Category:** Numerics
**Created:** [March 9, 2018, 8:09pm UTC](https://discourse.julialang.org/t/special-method-for-finding-eigenvalues-of-a-large-sparse-symmetric-matrix/9621 "2018-03-09T20:09:05Z")
**Posts on this page:** 1
**Showing post:** 13

<div class="post-metadata">

### Author: ![stevengj](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/stevengj/32/71_2.png) [@stevengj](https://discourse.julialang.org/u/stevengj)
#### Post date: [March 11, 2018, 12:05am UTC](https://discourse.julialang.org/t/special-method-for-finding-eigenvalues-of-a-large-sparse-symmetric-matrix/9621/13 "2018-03-11T00:05:51Z")

</div>

10% fill is huge. There is usually no point in using a sparse solver if you have that many nonzero entries. (On the order of 10 nonzero entries per row is common in real sparse-matrix applications, which corresponds to \< 0.1% fill for a 14000x14000 matrix.)

And sparse-direct solvers will generally perform poorly for random fill. The algorithms work best for sparsity that comes from local interactions on a mesh or grid.

1d grids are best, and 2d grids/meshes are still very good. For 3d grids, the scaling of sparse-direct methods is worse (this is a consequence of the difficulty of partitioning meshes in higher dimensions, essentially…see e.g. Davis’ book on sparse-direct methods). For very large 3d problems you usually have to switch to purely iterative methods (GMRES, CG, etc) and hope you can find a good preconditioner.

---

_[View the full topic](https://discourse.julialang.org/t/special-method-for-finding-eigenvalues-of-a-large-sparse-symmetric-matrix/9621)._