Generalized conjugate gradient method for solving multilinearsystems

Let L be a real linear operator with a positive de nite symmetric part M. In certainapplications, several problems of the form M⋆N Y = can be solved with less human orcomputational effort than the original equation L⋆N = F. In this paper, the generalizedconjugate gradient method of Concus and Golub [Lecture Notes in Economics and Math-ematical Systems ۱۳۴, Springer-Verlag, New York, ۱۹۷۶] and Widlund [SIAM J. Numer.Anal., ۱۵ (۱۹۷۸), pp. ۸۰۱-۸۱۲] is extended for solving some tensor equations via Einsteinproduct. An example is also provided to show the efficiency of the proposed method. Finally,some concluding remarks are given.

Keywords:

Generalized conjugate gradient method , Tensor , Multilinear systems