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My method needs to solve the following problem. $$A = (B^{-1} + C^{-1} - D^{-1})^{-1}$$

Is there any way to rewrite this to avoid "too much" matrix inverse when implementing this in python?
The matrices are all symmetric and positive.

Gunhild
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1 Answers1

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You can multiply both sides of the equation by $(B^{-1}+C^{-1}-D^{-1})$ and get $$(B^{-1}+C^{-1}-D^{-1})A = I$$ thus getting rid of the "inverse of sum" part.

But I don't think you can avoid calculating the inverses of $B,C$ and $D$.

Nick202
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