An efficient Total Least Squares algorithm based on a rank-revealing two-sided orthogonal decomposition

Abstract

Solving Total Least Squares (TLS) problemsAX≈B requires the computation of the noise subspace of the data matrix [A;B]. The widely used tool for doing this is the Singular Value Decomposition (SVD). However, the SVD has the drawback that it is computationally expensive. Therefore, we consider here a different so-called rank-revealing two-sided orthogonal decomposition which decomposes the matrix into a product of a unitary matrix, a triangular matrix and another unitary matrix in such a way that the effective rank of the matrix is obvious and at the same time the noise subspace is exhibited explicity. We show how this decompsition leads to an efficient and reliable TLS algorithm that can be parallelized in an efficient way.