Stabilization of cyclic subspace regression

Developments that produced a stable numerical algorithm for cyclic subspace regression (CSR) are described. This simple algorithm produces solutions for principal component regression, partial least squares, least squares, and other related intermediate regression methodologies by exactly the same procedure. The development begins with a theoretical CSR algorithm that should produce accurate results. However, when used in numerical form, it does not produce accurate results because numbers are generated which are too small for most computational tools to accurately represent. Several strategies to deal with this numerical instability are described. Results obtained using each approach are reported as applied to two data sets. The development ends with presentation of the stable algorithm as well as MATLAB code for the algorithm.