The partial total least squares algorithm

Abstract

In this paper, an improved algorithm PTLS for solving total least squares (TLS) problems AX ≈ B is presented. As only a basis of the right singular subspace associated with the smallest singular values of the data [A; B] is needed, the computational cost can be reduced considerably by using the partial SVD algorithm. This algorithm computes in an efficient way a basis for the left and/or right singular subspace of a matrix associated with its smallest singular values. An analysis of the operation counts, as well as computational results, show the relative efficiency of PTLS with respect to the classical TLS algorithm. Typically, PTLS reduces the computation time with a factor 2. © 1988.