Detection of structural inconsistency in systems of equations with degrees of freedom and its applications
type: Item
instance of: scholarly article
title: Detection of structural inconsistency in systems of equations with degrees of freedom and its applications
zbMATH Open document ID: 0572.65050
DOI: 10.1016/0166-218X(85)90051-4
author: K. Sugihara
published in: Discrete Applied Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The concept of structural inconsistency of equations is studied with regard to analysis of large-scale engineering systems. The concept of structural inconsistency of systems of equations, where the number of equations equals that of unknowns, is generalized to systems, where the number of unknowns is greater than that of equations (due to degrees of freedom of their solution). Starting from the matroid theory a theorem is proven which relates the consistency of a primary structure to the maximum flow of the associated network. Based on this result two algorithms are presented for efficient detection of inconsistency in the systems of equations. Some examples illustrating applications of the algorithms for analyzing various engineering problems (e.g. line drawings of polyhedrons, dimensioning in engineering drawings or general linked structures) are presented. Analysis of time complexity shows that the presented method is useful both for detecting errors in formulation of large-scale systems of equations and for analyzing some essential properties of various engineering systems.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C35
Mathematics Subject Classification ID: 94C15
Mathematics Subject Classification ID: 68R10
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 3913574
zbMATH Keywords: large-scale systems
zbMATH Keywords: structural inconsistency
zbMATH Keywords: matroid
MaRDI profile type: Publication
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full work available at URL: 0166-218x(85)90051-4
OpenAlex ID: W2021394402
description: scientific article; zbMATH DE number 3913574