A comparison of some methods for bounding connected and disconnected solution sets of interval linear systems |
| |
Authors: | R Baker Kearfott |
| |
Affiliation: | (1) Department of Mathematics, University of Louisiana, U.L. Box 4-1010, Lafayette, LA 70504-1010, USA |
| |
Abstract: | Summary Finding bounding sets to solutions to systems of algebraic equations with uncertainties in the coefficients, as well as rapidly
but rigorously locating all solutions to nonlinear systems or global optimization problems, involves bounding the solution
sets to systems of equations with wide interval coefficients. In many cases, singular systems are admitted within the intervals
of uncertainty of the coefficients, leading to unbounded solution sets with more than one disconnected component. This, combined
with the fact that computing exact bounds on the solution set is NP-hard, limits the range of techniques available for bounding
the solution sets for such systems. However, the componentwise nature and other properties make the interval Gauss–Seidel
method suited to computing meaningful bounds in a predictable amount of computing time. For this reason, we focus on the interval
Gauss–Seidel method. In particular, we study and compare various preconditioning techniques we have developed over the years
but not fully investigated, comparing the results. Based on a study of the preconditioners in detail on some simple, specially–designed
small systems, we propose two heuristic algorithms, then study the behavior of the preconditioners on some larger, randomly
generated systems, as well as a small selection of systems from the Matrix Market collection.
|
| |
Keywords: | 65F10 65G20 65K99 |
本文献已被 SpringerLink 等数据库收录! |
|