A comparison of three numerical methods for updating regressions.

Abstract

Three numerical procedures are presented for updating regressions. All three methods are based on QR factorization, but after that they use different philosophies to update the regression coefficients. Elden's algorithm updates using only the triangular matrix R. This procedure does not use orthogonal transformations, but it uses hyperbolic rotations. The modified Gram-Schmidt QR process is used by Gragg- Leveque-Trangenstein's method where the matrix with orthonormal columns is stored and updated. Chan's algorithm computes a column permutation n and a QR factorization of a matrix A such that a rank deficiency of A will be revealed. Although the three methods are based on different ideas and can be used for different purposes their comparison shows that Chan's algorithm is the only accurate one in the rank deficient case, and that Gragg-Leveque-Trangenstein's method is the cheapest and the most stable.