Solution of linear systems in the TT-format

05/05/2011

The new paper, S.V. Dolgov, I.V. Oseledets, Solution of linear systems and matrix inversion in the TT-format describes a DMRG-type method for the solution of linear systems with both the matrix and the tensor in the TT-format. The method is able to solve certain structured linear systems of order 2^d, where d can be of order several hundreds, and TT-ranks can be of order tensor or hundreds. The solver is available as a part of the TT-Toolbox 2.1. Moreover, some test data of the article can be downloaded (the new Toolbox is required to be installed). You can download it from the page Benchmarks and data or [drain file 8 url directly download test data as gzipped tar archive] This archive contains .mat files with A,x,rhs, where A is a TT-matrix, rhs is a TT-vector (TT-tensor), x is an approximate solution of A*x = rhs. You can check this directly by computing in MATLAB norm(A*x — rhs)/norm(rhs) Be aware, that computing full(A) is prohibitive for all examples, but full(x) or full(rhs) sometimes is not! I plan to add more benchmarking data to this page, with more TT-matrices and TT-vectors.

News

26/05/2016 A TT-eigenvalue solver that finally works
12/05/2016 Exponential machines and tensor trains
06/04/2016 Convergence analysis of a projected fixed-point iteration
30/03/2016 Compress-and-eliminate solver for sparse matrices
01/12/2015 New paper in SIMAX

Contact

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