Talk:Putzer Algorithm

Does anyone know who Putzer was/is? I can find no citations anywhere. --Prime.mover 21:39, 15 April 2010 (UTC)

It took some wicked googling, but I found out he is probably E.J. Putzer, a dude from the North American Aviation Science Center way back when, and the official citation would Avoiding the Jordan canonical form in the discussion of linear systems with constants coefficients, American Mathematical Monthly, 73, (1966), pp. 2–7. See .Colors


 * Delightful. Thx.--Prime.moverd 19:23, 19 April 2010 (UTC)

2020: The original 1966 article is available on Google Scholar [] The most-used instance of Putzer's theorem is n=2, which gives rise to three formulas for $e^{At}$ ordered by the character of the roots of the characteristic equation. The formulas are distinct from but similar to the classical spectral formulas for $e^{At}$ cited in linear algebra references. The first identity below is also valid for complex eigenvalues. The other two can be derived on the fly from the first by either limiting $\lambda_2 \to \lambda_1$ or taking real parts.

Real $\lambda_1\ne\lambda_2$: $\quad\displaystyle e^{At}=e^{\lambda_1 t}I + \frac{e^{\lambda_2 t}-e^{\lambda_1 t}}{\lambda_2-\lambda_1} (A-\lambda_1 I)$

Real $\lambda_1=\lambda_2$: $\quad\displaystyle e^{At}=e^{\lambda_1 t}I+ te^{\lambda_1 t}(A-\lambda_1 I)$

Complex $\lambda_1=\bar\lambda_2$, $\lambda_1=a+bi$, $b>0$: $\quad\displaystyle e^{At}=e^{at}\cos bt\,I + \frac{e^{at}\sin(bt)}{b}(A-aI)$

These special identities could make an example page with a derivation from Putzer's formula.--Gbgustafson (talk) 04:33, 16 January 2020 (EST)