Description
A time-evolving physical situation may be approximated by the action of a linear operator to the instantaneous state vector.
The dynamic mode decomposition strives to approximate the evolution operator from a known sequence of observations, . Thus, we ask the following matrix equation to hold:
The right hand side states that is a linear combination of the columns of, which can be expressed as
where S is the companion matrix
The matrix S is small as compared to the sample data V. Therefore eigenvalues and eigenvectors can be computed with ease.
Read more about this topic: Dynamic Mode Decomposition
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