Alternating minimal energy methods for linear systems in higher dimensions. Part II: Faster algorithm and application to nonsymmetric systems

Understand

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions.

• In [arXiv:1301.6068] this problem is approached by alternating minimization of the energy function, which we combine with steps of the basis expansion in accordance with the steepest descent algorithm.
• In this paper we combine the same steps in such a way that the resulted algorithm works with one or two neighboring cores at a time.
• The recurrent interpretation of the algorithm allows to prove the global convergence and to estimate the convergence rate.