HOBi-CGSTAB and HOBi-CRSTAB methods for solving some tensor equations.

Recently, solving tensor equations (or multilinear systems) has attracted a lot of attention. This paper investigates the tensor form of the Bi-CGSTAB and Bi-CRSTAB methods, by employing Kronecker product, vectorization, and bilinear operator, to solve the generalized coupled Sylvester tensor equations ∑ i = 1 n (X × 1 A i 1 × 2 A i 2 + Y × 1 B i 1 × 2 B i 2) = E 1 , ∑ i = 1 n (X × 1 C i 1 × 2 C i 2 + Y × 1 D i 1 × 2 D i 2) = E 2 , with no matricization. Also some properties of the new methods are presented. By applying multilinear operator, the proposed methods are extended to the general form. Some numerical examples are provided to compare the efficiency of the investigated methods with some existing popular algorithms. Finally, some concluding remarks are given. [ABSTRACT FROM AUTHOR]