Symbolic derivative in a sum

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uranus 2024-3-14

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评论： David Goodmanson 2024-3-15

I have this expression

and I want to evaluate the derivative over p where A_m has a form like that:

It don't know even where to start from. Is there any way to do it ?

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Answer 1

David Goodmanson 2024-3-14

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编辑：David Goodmanson 2024-3-14

在 MATLAB Online 中打开

Hello OG,

If you know d/dp G for the elements of G, you can use

d/dp G^-1 = -G^-1 (d/dp G) G^-1

which is all right numerically, But if you want to do the whole thing symbolically, unless the size of G is really small this will turn into a huge intractable mess of symbolic spaghetti very quickly.

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uranus 2024-3-14

编辑：uranus 2024-3-14

I have already tried that, but then it turns into (also a mess of) normal differentiation, but I can write it explicitly. Thus, is it not anymore symbolic, right? The system is of the order of 20 but I think this is sufficient to get the spaghetti!

David Goodmanson 2024-3-15

If you know (d/dp G) either symbolically or numerically then you can get it numerically, and after that it would appear that numerical evaluation of the expression -G^-1 (d/dp G) G^-1 for a 20x20 should work reasonably well, unless G is close to being singular and has a bad condition number..

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