Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

An extended Krylov-like method for the solution of multi-linear systems

Abstract : In the present work, numerical methods for the solution of multi-linear system are presented. Most large-scale multi-linear solvers rely on either the alternating leastsquares or low rank Krylov methods. The approach we use to develop our methods lies somehow in between and can be considered as a generalisation of an alternated direction method. Given the multi-linear operator in the form of a sum of Kronecker product of matrices, we solve at each iteration a linear system for each summand. The approximate solution is then defined to be the best linear combination of these solutions, as well as the previous solution and the residual. Some convergence results are proved. Numerical experiments on two problems arising from parametric PDEs show the effectiveness of the proposed method.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

https://hal.inria.fr/hal-03374966
Contributor : Damiano Lombardi Connect in order to contact the contributor
Submitted on : Tuesday, October 12, 2021 - 2:10:27 PM
Last modification on : Thursday, October 14, 2021 - 3:36:11 AM

File

AD_paper.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03374966, version 1

Citation

Hussam Al Daas, Damiano Lombardi. An extended Krylov-like method for the solution of multi-linear systems. 2021. ⟨hal-03374966⟩

Share

Metrics

Record views

57

Files downloads

74