Equation-oriented system: an efficient programming approach to solve multilinear and polynomial equations by the conjugate gradient algorithm

The factor analysis problem can be conceptualized as an expansion of polynomial equations that are solvable using least-squares methods. The equation-oriented system (EOS) is introduced as a method for solving polynomial equations using a preconditioned conjugate gradient (CG) algorithm for the normal equations. EOS is a fast, easy to program, low computer memory requirement method for accomplishing this task. EOS can be used to solve multilinear and PARAFAC problems. The practical aspects of implementing EOS in MATLAB are discussed.