#### Publication Date

9-3-2013

#### Abstract

When trying to solve elliptical problems such as the Poisson problem on complicated domains, one procedure is to split the domain into a union of simpler subdomains. When solving these problems iteratively, it becomes important to be able to precondition the coupling between the subdomains. Using the Poisson problem as a test case, this thesis explores one idea for preconditioning this coupling, an idea based on interpolative decomposition and random matrices. We find that this procedure does create an efficient preconditioner to get at the coupling between subdomains.

#### Degree Name

Mathematics

#### Level of Degree

Masters

#### Department Name

Mathematics & Statistics

#### First Advisor

Lau, Stephen

#### First Committee Member (Chair)

Stephen Lau

#### Second Committee Member

Daniel Appelö

#### Third Committee Member

Evangelos A. Coutsias

#### Project Sponsors

National Science Foundation

#### Language

English

#### Keywords

Linear systems--Mathematical models, Decomposition (Mathematics), Iterative methods (Mathematics), Random matrices.

#### Document Type

Thesis

#### Recommended Citation

Quintana, Ambrose. "Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem." (2013). https://digitalrepository.unm.edu/math_etds/43