Guaranteed a posteriori error bounds for low rank tensor approximate solutions
| Type of publication: | Misc |
| Citation: | |
| Publication status: | Submitted |
| Year: | 2019 |
| Abstract: | 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-di usion problems. The error bound is obtained from Euler{Lagrange equations for a complementary ux 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 Schrodinger equation with the Henon-Heiles potential in up to 40 dimensions are presented to illustrate the eciency of this approach. |
| Preprint project: | NCMM |
| Preprint year: | 2019 |
| Preprint number: | 03 |
| Preprint ID: | NCMM/2019/03 |
| Keywords: | |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
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