Bounds for an estimate of the optimal backward error for linear least squares problems

Abstract

Algorithms for calculating sequences of upper and lower bounds for an estimate of the optimal backward error for linear least squares problems are developed, based on the Gauss quadrature theory. Numerical results show that the bounds converge quickly and are therefore useful in practice.

Keywords:

• optimal backward error
• least squares
• Gauss quadrature
• Lanczos tridiagonalization

2000 AMS Subject Classifications :

• 65F05
• 65F10
• 65F30
• 62J05