# On Coarse Grid Correction Methods in Krylov Subspaces

## Abstract

Two approaches using coarse grid correction in the course of a certain Krylov iterative process are presented. The aim of the correction is to accelerate the iterations. These approaches are based on an approximation of the function sought for by simple basis functions having finite supports. Additional acceleration can be achieved if the iterative process is restarted and the approximate solution is refined. In this case, the resulting process turns out to be a two-level preconditioned method. The influence of different parameters of the iterative process on its convergence is demonstrated by numerical results.

- Authors:

- Institute of Computational Mathematics and Mathematical Geophysics SO RAS (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22773929

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 232; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; CONVERGENCE; CORRECTIONS; FUNCTIONS; GRIDS; ITERATIVE METHODS; NUMERICAL SOLUTION

### Citation Formats

```
Gurieva, Y. L., E-mail: yana@lapasrv.sscc.ru, and Il’in, V. P., E-mail: ilin@sscc.ru.
```*On Coarse Grid Correction Methods in Krylov Subspaces*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3907-9.

```
Gurieva, Y. L., E-mail: yana@lapasrv.sscc.ru, & Il’in, V. P., E-mail: ilin@sscc.ru.
```*On Coarse Grid Correction Methods in Krylov Subspaces*. United States. doi:10.1007/S10958-018-3907-9.

```
Gurieva, Y. L., E-mail: yana@lapasrv.sscc.ru, and Il’in, V. P., E-mail: ilin@sscc.ru. Wed .
"On Coarse Grid Correction Methods in Krylov Subspaces". United States. doi:10.1007/S10958-018-3907-9.
```

```
@article{osti_22773929,
```

title = {On Coarse Grid Correction Methods in Krylov Subspaces},

author = {Gurieva, Y. L., E-mail: yana@lapasrv.sscc.ru and Il’in, V. P., E-mail: ilin@sscc.ru},

abstractNote = {Two approaches using coarse grid correction in the course of a certain Krylov iterative process are presented. The aim of the correction is to accelerate the iterations. These approaches are based on an approximation of the function sought for by simple basis functions having finite supports. Additional acceleration can be achieved if the iterative process is restarted and the approximate solution is refined. In this case, the resulting process turns out to be a two-level preconditioned method. The influence of different parameters of the iterative process on its convergence is demonstrated by numerical results.},

doi = {10.1007/S10958-018-3907-9},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 6,

volume = 232,

place = {United States},

year = {2018},

month = {8}

}

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