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 134, Springer-Verlag, New York, 1976] and Widlund [SIAM J. Numer.Anal., 15 (1978), pp. 801-812] 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.

کلیدواژه های Generalized conjugate gradient method for solving multilinearsystems:

Generalized conjugate gradient method ، Tensor ، Multilinear systems