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# SMAS Seminar Series

## September 7, 2017 @ 1:30 pm - 2:30 pm

##### Speaker

Dr Marianito Rodrigo

##### Title

On Putzer’s method for bounded linear operators

##### Abstract

Putzer (1966) introduced an elementary technique for computing the matrix exponential, and involves the solution of a linear first-order ODE.

This technique was extended by Elaydi and Harris (1998) to compute a matrix power. In this case one has to solve a linear first-order difference equation.

Recently, Rodrigo (2016) introduced analogues of the matrix exponential for fractional time-derivative operators and extended Putzer’s method to compute these “fractional” matrix exponentials.

The above problems can be formulated as finding the solution x of an equation of the form L x = A x, where A is a square matrix and L is the corresponding time evolution operator.

In this talk I will extend Putzer’s method to the case when L and A are appropriate bounded linear operators on a Banach space X. The above three examples are recovered as special cases when X is Euclidean space. Other applications include linear eigenvalue problems and operator exponentials