What is the difference between Matrix Exponential and Taylor Series?

Hi

I would like to know how matlab calculates Matrix Exponential (command expm()). I do understand it calculates based on Taylor Series. The question is,as to how many terms MATLAB calculates? On dealing with 2nd and higher order terms for State transition Matrix, MATLAB produces huge number matrix. Is there way to reduce the size of state transition Matrix?

Answer 1

[Matt J]

doc expm says that it uses the Padé approximation, rather than a Taylor approximation, and gives this as a reference.

Higham, N. J., "The Scaling and Squaring Method for the Matrix Exponential Revisited," SIAM J. Matrix Anal. Appl., 26(4) (2005), pp. 1179–1193.

[Rock]

Thanks Matt!!

On using second order for calculation of state transition matrix using( expm()), is there way to reduce to second term approximation?

[Matt J]

 expmA_taylor2 = polyvalm( [0.5 1 1],A);