#### Date of Award

2014-01-01

#### Degree Name

Master of Science

#### Department

Mathematical Sciences

#### Advisor(s)

Piotr Wojciechowski

#### Abstract

There are known necessary and sufficient conditions for a subspace of Rm to be lattice-ordered. Let Y = {y1,…,ym} and yi are rows of the matrix X. A subspace ⟨X⟩, of linear space generated by the set X of n linearly independent positive vectors is lattice-ordered if and only the set X admits a fundamental set of indices I, which means that the subset YI ⊆ Y of vectors indexed by I is linearly independent, and every vector from Y\YI is a nonnegative linear combination of vectors form YI.

In economics it is possible to prove that the minimum-cost insured portfolio exists if and only if the linear space generated by the corresponding financial instruments is lattice-ordered.

In the literature there are known algorithms with exponential complexity that determine if a given subspace is lattice-ordered.

In this Thesis a polynomial time algorithm (serial and parallel) as well as its computer implementation will be presented. The method can be applied in economics as well as in the theory of vector lattices.

#### Language

en

#### Provenance

Received from ProQuest

#### Copyright Date

2014

#### File Size

67 pages

#### File Format

application/pdf

#### Rights Holder

Andrew Martin Pownuk

#### Recommended Citation

Pownuk, Andrew Martin, "Fast Algorithm For Finding Lattice Subspaces In Rn And Its Implementation" (2014). *Open Access Theses & Dissertations*. 1329.

https://digitalcommons.utep.edu/open_etd/1329