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In practical applications, incremental tensors are very common: only a portion of tensor data is available, and new data are arriving in the next time step or continuously over time. To handle this type of tensors time-saving algorithms are required for online computation. In this paper, we consider incremental CP ( CANDECOMP/PARAFAC ) decomposition, which requires one to update the CP decomposition after new tensor data, together with the exiting tensor, are ready for analysis. There exist several incremental CP decomposition algorithms, but almost all of these algorithms assume that the number of CP decomposition components remains fixed in the incremental process. The main contribution of this paper is the study of how to add components in the incremental CP decomposition. We derive the coordinate representation of the incremental CP decomposition with respect to a special basis and show related properties of tensor rank and the uniqueness of such incremental CP decomposition. Under the framework of this representation, the proposed method can be solved by using an alternating minimization algorithm. Numerical examples are presented to show the good performance of the proposed algorithms in terms of computational time and data fitting compared with existing methods. [ABSTRACT FROM AUTHOR]

We consider the iterative solution of weighted Toeplitz least squares problems. Our approach is based on an augmented system formulation. We focus our attention on two types of preconditioners: a variant of constraint preconditioning, and the Hermitian/skew-Hermitian splitting (HSS) preconditioner. Bounds on the eigenvalues of the preconditioned matrices are given in terms of problem and algorithmic parameters, and numerical experiments are used to illustrate the performance of the preconditioners. [ABSTRACT FROM AUTHOR]