A faster implementation of Markowitz' pivot rule in LU factorization

[vandenheuvel]

Markowitz' rule is a decision rule that chooses the next pivot during LU decomposition in a way that reduces fill-in. It doesn't take numerical stability into account, but for arbitrary precision, that doesn't matter. It minimizes an upper bound on fill-in by choosing a row and column with a non-zero that have minimal (nnz(row) - 1) * (nnz(column) - 1).

A fast search for the row and column that minimize the above value (while minimizing column swaps) would improve runtime.