Further improvements of the speed of the Tucker3 three-way algorithm

An improvement to the Andersson–Bro (A-B) alternating least squares (ALS) algorithm for the Tucker3 three-way model is presented. The published A-B algorithm deals cyclically with the three modes of the problem. In each ALS substep, the whole array is projected onto a different mode. The projections are the dominating workload. In the improved version, each whole-array projection is utilized for two ALS substeps. The same ALS steps are performed as before but the number of full-sized projections is cut to half. This almost doubles the speed of the algorithm without changing its convergence properties. The possibility to utilize each full-sized projection for more than two ALS substeps is discussed.