Create a triangular solver

[tbetcke]

Triangular solves are a core task of many more advanced matrix algorithms. We want to implement.

• A simple serial triangular solve.
• A multithreaded triangular solve using a threadpool.

The multithreaded version also requires serial triangular solves. So it is natural that both needs to be done.
A precondition for this issue is a decision on the parallelization framework in #11 .

[strasdat]

Once we have a triangular solver, I might be motivated to implement a dense LDL (https://en.wikipedia.org/wiki/Cholesky_decomposition#LDL_decomposition) decomposition, to solve linear systems Ax=b, with A being positive semi-definite.

[tbetcke]

Sounds good. My goal for Householder is that eventually we have modern task based algorithms for all decompositions. For LDL^T see for example (https://hal.inria.fr/hal-00809663/document). However,

• we still want single core algorithms as well (lots of applications where you want to do small decompositions within a thread and not have your linear algebra spread out of all threads)
• Also for parallel algorithms we usually need to single core versions as components.