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The computation of the exponential and logarithmic mappings and their first and second linearizations

Ortiz, M. and Radovitzky, R. A. and Repetto, E. A. (2001) The computation of the exponential and logarithmic mappings and their first and second linearizations. International Journal for Numerical Methods in Engineering, 52 (12). pp. 1431-1441. ISSN 0029-5981. https://resolver.caltech.edu/CaltechAUTHORS:20171128-144521153

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Abstract

We describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the Taylor expansion and the spectral representation. We also provide guidelines for switching between those representations on the basis of the size of the argument. The first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations. This representation does not require the use of perturbation formulae for eigenvalues and eigenvectors. Our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://dx.doi.org/10.1002/nme.263DOIArticle
http://onlinelibrary.wiley.com/doi/10.1002/nme.263/abstractPublisherArticle
Additional Information:© 2001 John Wiley & Sons. Received 20 April 2000. Revised 20 February 2001.
Group:GALCIT
Subject Keywords:exponential and logarithmic mappings; linearization; finite element analysis
Issue or Number:12
Record Number:CaltechAUTHORS:20171128-144521153
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171128-144521153
Official Citation:Ortiz, M., Radovitzky, R. A. and Repetto, E. A. (2001), The computation of the exponential and logarithmic mappings and their first and second linearizations. Int. J. Numer. Meth. Engng., 52: 1431–1441. doi:10.1002/nme.263
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83547
Collection:CaltechAUTHORS
Deposited By: Lydia Suarez
Deposited On:28 Nov 2017 23:05
Last Modified:03 Oct 2019 19:07

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