Description:
<jats:title>Abstract</jats:title><jats:p>We discuss discrete‐time dynamical systems depending on a parameter μ. Assuming that the system matrix <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0001.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0001" /> is given, but the parameter μ is unknown, we infer the most‐likely parameter <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0002.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0002" /> from an observed trajectory <jats:italic>x</jats:italic> of the dynamical system. We use parametric eigenpairs <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0003.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0003" /> of the system matrix <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0004.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0004" /> computed with Newton's method based on a Chebyshev expansion. We then represent <jats:italic>x</jats:italic> in the eigenvector basis defined by the <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0005.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0005" /> and compare the decay of the components with predictions based on the <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0006.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0006" />. The resulting estimates for μ are combined using a kernel density estimator to find the most likely value for <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/pamm202300122-math-0007.png" xlink:title="urn:x-wiley:16177061:media:pamm202300122:pamm202300122-math-0007" /> and a corresponding uncertainty quantification.</jats:p>