Publication detail

Numerical matrix exponential function derivative via Laplace transform approach

BRANČÍK, L.

Original Title

Numerical matrix exponential function derivative via Laplace transform approach

English Title

Numerical matrix exponential function derivative via Laplace transform approach

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

matrix exponential function, derivative, Laplace transform, numerical inversion, sensitivity

RIV year

2009

Released

11.02.2009

Publisher

ARGESIM / ASIM

Location

Vídeň

ISBN

978-3-901608-35-3

Book

Proceedings MATHMOD 09 Vienna, Full Papers CD Volume

Pages from

2612

Pages to

2615

Pages count

4

URL

BibTex


@inproceedings{BUT32711,
  author="Lubomír {Brančík}",
  title="Numerical matrix exponential function derivative via Laplace transform approach",
  annote="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.",
  address="ARGESIM / ASIM",
  booktitle="Proceedings MATHMOD 09 Vienna, Full Papers CD Volume",
  chapter="32711",
  howpublished="electronic, physical medium",
  institution="ARGESIM / ASIM",
  year="2009",
  month="february",
  pages="2612--2615",
  publisher="ARGESIM / ASIM",
  type="conference paper"
}