About LU factorization

[Werner]

In my time (admittedly a while ago..), Crout LU-factorisation reordered the operations so that each element (in L or U) was computed using a dot product. Using floating-2 (showing my age) or, in the 42S/48S world, 15-digit intermediate results, one could obtain far better results at almost no cost.
Crout factorisation alternatingly computes a row and a column. In that sense, the 42S/48S algorithms (while being 'Doolittle factorisations') are also Crout factorisation as they do use 15-digit dot products. Don't know what the Prime does, however.
The 48G and onwards (up till, and including, the 50g) use 15 digits for all their matrix computations (the matrix is first converted to 15 digits, then all operations are performed, then it is rounded back to 12 digits).
Cheers, Werner