The triangular matrices of Gaussian elimination and related decompositions

It has become commonplace that triangular systems are solvedto higher accuracy than their condition would warrant. Thisobservation is not true in general, and counterexamples areeasy to construct. However, it is often true of the triangularmatrices from pivoted LU or QR decompositions. It is shown thatthis fact is closely connected with the rank-revealing characterof these decompositions. ^* This report is available by anonymous ftp from thales.cs.umd.eduin the directory pub/reports.