Error-free computation of the moore-penrose inverse with application to linear least squares analysis

Abstract

The paper develops a numerical method which allows error-free computation of the Moore-Penrose inverse of a matrix having rational elements. Multiple modulus residue arithmetic is used to avoid error that is inherent in floating-point arithmetic. The method is an improved form of one originally presented by Stallings and Boullion (1972).

Keywords:

• Exact inverse
• multiple modulus arithmetic
• error-free linear least squares