About: Numerical matrix exponential function derivative via Laplace transform approach

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Description	The paper deals with a method how to determine a derivative of a matrix exponential function with respect to a parameter inside a matrix of the exponent. The considered technique is based on a Laplace transform approach when, in the transform domain, the derivative is easily stated. To get a result in the original domain, however, it is necessary to use some numerical technique of an inverse Laplace transform (NILT). In the paper, two such methods are presented. To ensure numerical stability of the computation the NILT method is always preceeded by scaling to decrease a Euclidean norm of the matrix below a predefined value, and followed by squaring to return it to the original value. The method finds its practical application in various fields of the electrical engineering simulation, e.g. for a sensitivity analysis in systems with multiconductor transmission lines as their distributed parts. The paper deals with a method how to determine a derivative of a matrix exponential function with respect to a parameter inside a matrix of the exponent. The considered technique is based on a Laplace transform approach when, in the transform domain, the derivative is easily stated. To get a result in the original domain, however, it is necessary to use some numerical technique of an inverse Laplace transform (NILT). In the paper, two such methods are presented. To ensure numerical stability of the computation the NILT method is always preceeded by scaling to decrease a Euclidean norm of the matrix below a predefined value, and followed by squaring to return it to the original value. The method finds its practical application in various fields of the electrical engineering simulation, e.g. for a sensitivity analysis in systems with multiconductor transmission lines as their distributed parts. (en)
Title	Numerical matrix exponential function derivative via Laplace transform approach Numerical matrix exponential function derivative via Laplace transform approach (en)
skos:prefLabel	Numerical matrix exponential function derivative via Laplace transform approach Numerical matrix exponential function derivative via Laplace transform approach (en)
skos:notation	RIV/00216305:26220/09:PU80931!RIV10-MSM-26220___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM0021630503)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Brančík, Lubomír
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Vysoké učení technické v Brně / Fakulta elektrotechniky a komunikačních technologií
http://linked.open...dnocenehoVysledku	330213
http://linked.open...ai/riv/idVysledku	RIV/00216305:26220/09:PU80931
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	matrix exponential function, derivative, Laplace transform, numerical inversion, sensitivity (en)
http://linked.open.../riv/klicoveSlovo	numerical inversion derivative Laplace transform sensitivity matrix exponential function
http://linked.open...ontrolniKodProRIV	[C059795068DC]
http://linked.open...v/mistoKonaniAkce	Vídeň
http://linked.open...i/riv/mistoVydani	Vídeň
http://linked.open...i/riv/nazevZdroje	Proceedings MATHMOD 09 Vienna, Full Papers CD Volume
http://linked.open...in/vavai/riv/obor	JA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...UplatneniVysledku	2009
http://linked.open...iv/tvurceVysledku	Brančík, Lubomír
http://linked.open...vavai/riv/typAkce	WRD - Světová
http://linked.open.../riv/zahajeniAkce	2009-02-11 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Nové trendy v mikroelektronických systémech a nanotechnologiích (MIKROSYN)
number of pages	4 (xsd:int)
http://purl.org/ne...btex#hasPublisher	ARGESIM / ASIM
https://schema.org/isbn	978-3-901608-35-3
http://localhost/t...ganizacniJednotka	26220
is http://linked.open...avai/riv/vysledek of	Numerical matrix exponential function derivative via Laplace transform approach Numerical matrix exponential function derivative via Laplace transform approach Numerical matrix exponential function derivative via Laplace transform approach Numerical matrix exponential function derivative via Laplace transform approach

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