Abstracts: Michael Saunders
Some sparse LU considerations
John Reid's LA05 software showed that the Bartels-Golub update could be implemented efficiently for sparse matrices. It strongly influenced the development of LUSOL, the engine for the large-scale optimization solvers MINOS, SNOPT, and lp_solve.
To gain rank-revealing properties, LUSOL implements threshold versions of rook pivoting and complete pivoting. In contrast to the folklore for complete pivoting, the cost of tracking the largest remaining nonzero is negligible (with the help of a heap data structure). We consider the value of tracking "Amax" for all of the threshold pivoting options.
We also review some of John's other invaluable contributions to scientific computing.