Add tutorial on interpolation for LTI systems #2153
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pmli
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Aug 18, 2023
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pmli
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- interpolation at infinity
- interpolation at zero
- interpolation at a non-zero finite point
- tangential interpolation
- structure-preserving interpolation?
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I really like the structure of the tutorial and the visualization of the different interpolation approaches, but I think a few details can be added. I would say structure-preserving interpolation and structure-preserving model reduction (e.g., second order models) for that matter could be treated in a separate tutorial.
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| to perform a (Petrov-)Galerkin projection. | ||
| This will achieve interpolation of the first $2 r$ moments at infinity |
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I think there should be a few more details here. For example, what does the transfer function or interpolated model look like exactly after using PG projection? Maybe the interpolation which is then achieved could be written down explicitly? For someone who is new to all this, it might be very helpful to have some of these basic facts appear here.
| (also known as the shifted Padé approximation). | ||
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| ```{math} | ||
| \newcommand{\H}{\operatorname{H}} |
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Running in binder I got the message "\newcommand{\H} attempting to redefine \H; use \renewcommand" and latex did not compile.
| one idea is to do interpolation at multiple points (sometimes called *multipoint Padé*), | ||
| whether of lower or higher-order. | ||
| pyMOR implements bitangential Hermite interpolation (BHI) for different types of {{ Models }}. | ||
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There should maybe again be another couple lines saying what bitangential means here or similarly some explanation of what b and c are in the code below.
| (higher-order interpolation at single point {cite}`G97`) and | ||
| then move on to bitangential Hermite interpolation | ||
| which is directly supported in pyMOR. | ||
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It would possibly be helpful to write a bit more motivation for interpolatory model reduction here or in the section below. Transfer functions are known from the LTI systems tutorial. By simply pointing out the relationship between the input-output mapping which we are interested in and the transfer function it will hopefully immediately make sense why we should even care about these interpolatory methods.
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