A fast non‐negativity‐constrained least squares algorithm

In this paper a modification of the standard algorithm for non‐negativity‐constrained linear least squares regression is proposed. The algorithm is specifically designed for use in multiway decomposition methods such as PARAFAC and N‐mode principal component analysis. In those methods the typical situation is that there is a high ratio between the numbers of objects and variables in the regression problems solved. Furthermore, very similar regression problems are solved many times during the iterative procedures used. The algorithm proposed is based on the de facto standard algorithm NNLS by Lawson and Hanson, but modified to take advantage of the special characteristics of iterative algorithms involving repeated use of non‐negativity constraints. The principle behind the NNLS algorithm is described in detail and a comparison is made between this standard algorithm and the new algorithm called FNNLS (fast NNLS). © 1997 John Wiley & Sons, Ltd.