A useful identitiy in circuit theory
type: Item
instance of: scholarly article
title: A useful identitiy in circuit theory
zbMATH Open document ID: 0828.15003
DOI: 10.1016/0016-0032(93)90064-2
author: Y. Zhu
author: Wai-Kai Chen
published in: Journal of the Franklin Institute
publication date: 1996-01-11T00:00:00Z
review text: A useful identity for circuit theory is obtained. The authors considered the linear system \(AX= B\), where \(A\) is a square matrix and \(X\) and \(B\) are column matrices. If \(B\) remains the same but an element of \(A\), say \(a_{ij}\), is modified, then it is asked to find the derivative of the perturbed solution \(X'\) with respect to the modified element. The result can be proved to be of much interest in sensitivity theory, Kron's method of tearing and \textit{F. H. Branin's} formulae [The relation between Kron's method and the classical methods of network analysis. Matrix Tensor Q. 12, 69-105 (1962)].
Mathematics Subject Classification ID: 15A06
Mathematics Subject Classification ID: 94C05
Mathematics Subject Classification ID: 93B35
zbMATH DE Number: 698772
zbMATH Keywords: matrix formulae
zbMATH Keywords: identity
zbMATH Keywords: circuit theory
zbMATH Keywords: sensitivity theory
zbMATH Keywords: Kron's method of tearing
reviewed by: Dumitru Stanomir
MaRDI profile type: Publication
full work available at URL: 0016-0032(93)90064-2
OpenAlex ID: W1995489414
cites work: Q3259278
cites work: A Survey of Some Closed Methods for Inverting Matrices
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description: scientific article; zbMATH DE number 698772