Nov 6 – 8, 2019
MPI Magdeburg
Europe/Berlin timezone

Guaranteed a posteriori error bounds for low rank tensor approximate solutions

Nov 6, 2019, 2:40 PM
25m
Prigogine (MPI Magdeburg)

Prigogine

MPI Magdeburg

MPI for Dynamics of Complex Technical Systems Sandtorstr. 1 39106 Magdeburg
Talk Talks Day I

Speaker

Sergey Dolgov (University of Bath, UK)

Description

We propose guaranteed and fully computable upper bound on the energy norm of the error in low rank Tensor Train (TT) approximate solutions of (possibly) high dimensional reaction-diffusion problems. The error bound is obtained from Euler-Lagrange equations for a complementary flux reconstruction problem, which are solved in the low rank TT representation using the block Alternating Linear Scheme. This bound is guaranteed to be above the energy norm of the total error, including the discretization error, the tensor approximation error, and the error in the solver of linear algebraic equations. Numerical examples with the Poisson equation and the Schroedinger equation with the Henon-Heiles potential in up to 40 dimensions will be presented to illustrate the efficiency of this approach.

Primary author

Sergey Dolgov (University of Bath, UK)

Co-author

Tomas Vejchodsky (Institute of Mathematics, Czech Academy of Sciences)

Presentation materials

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