QR Decomposition in Least Squares Analysis, with an Application to the Reduction of Rotational Spectra to Molecular Constants

Abstract

A QR decomposition and the modification of the Gram-Schmidt method in least-squares analysis are presented, as well as a detailed description of the numerical calculation of the rotational constants. The ordinary least-squares technique with the construction of normal equations and the corrected least-squares technique with QR decomposition are compared. These procedures were tested using well-defined synthetic data and the published microwave data on the CS₂. molecule.

Key Words:

• rotational constants
• QR decomposition
• least-squares fit