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Solving linear boundary value problems via non-commutative Groebner bases

Rosenkranz, Markus, Buchberger, Bruno, Engl, Heinz W. (2003) Solving linear boundary value problems via non-commutative Groebner bases. Applicable Analysis, 82 (7). pp. 655-675. ISSN 0003-6811. (doi:10.1080/0003681031000118981) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:29978)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL
http://dx.doi.org/10.1080/0003681031000118981

Abstract

A new approach for symbolically solving linear boundary

value problems is presented. Rather than using general-purpose tools

for obtaining parametrized solutions of the underlying ODE and fitting

them against the specified boundary conditions (which may be quite

expensive), the problem is interpreted as an operator inversion

problem in a suitable Banach space setting. Using the concept of the

oblique Moore-Penrose inverse, it is possible to transform the

inversion problem into a system of operator equations that can be

attacked by virtue of non-commutative Groebner bases. The resulting

operator solution can be represented as an integral operator having

the classical Green's function as its kernel. Although, at this stage

of research, we cannot yet give an algorithmic formulation of the

method and its domain of admissible inputs, we do believe that it has

promising perspectives of automation and generalization; some of these

perspectives are discussed.

Item Type: Article
DOI/Identification number: 10.1080/0003681031000118981
Uncontrolled keywords: Linear boundary value problems, Green's function, Moore-Penrose equations, symbolic solution
Subjects: Q Science > QA Mathematics (inc Computing science) > QA150 Algebra
Q Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equations
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Markus Rosenkranz
Date Deposited: 27 Jul 2012 18:00 UTC
Last Modified: 16 Nov 2021 10:07 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/29978 (The current URI for this page, for reference purposes)
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