%0 Journal Article %1 Ortiz2001 %A Ortiz, M %A Radovitzky, R. A. %A Repetto, E. A. %D 2001 %J International Journal for Numerical Methods in Engineering %K imported %N 12 %P 1431--1441 %T The computation of the exponential and logarithmic mappings and their first and second linearizations %U http://dx.doi.org/10.1002/nme.263 %V 52 %X 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. Copyright � 2001 John Wiley & Sons, Ltd.

@article{Ortiz2001, 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. Copyright � 2001 John Wiley & Sons, Ltd.}, added-at = {2009-08-01T18:40:48.000+0200}, author = {Ortiz, M and Radovitzky, R. A. and Repetto, E. A.}, biburl = {https://www.bibsonomy.org/bibtex/28ef5c09c8231b19f6716d19166424e8b/jaksonmv}, file = {:D\:\\Users\\Jaksonmv\\Documents\\papers\\Ortiz2001.pdf:PDF}, interhash = {ce5afa43233f159b3654e9b3501966d8}, intrahash = {8ef5c09c8231b19f6716d19166424e8b}, journal = {International Journal for Numerical Methods in Engineering}, keywords = {imported}, number = 12, owner = {ManfrediniV}, pages = {1431--1441}, timestamp = {2009-08-01T18:40:55.000+0200}, title = {The computation of the exponential and logarithmic mappings and their first and second linearizations}, url = {http://dx.doi.org/10.1002/nme.263}, volume = 52, year = 2001 }