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November 10th, 2015, 11:01 PM   #1
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Computation of matrix inverse: I + A

Let I be the identity matrix, and A be an invertible matrix. Suppose A^(-1) is given. How can we cheaply compute

(A + I)^(-1)

Can you help me find the right identity.

Thank you so much in advance.
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November 11th, 2015, 11:59 AM   #2
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Solve (A+I)B=I for B

For 1X1 matrix solve (a+1)b=1. It has no simple solution in terms of 1/a so OP is not generally solvable.
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November 12th, 2015, 05:05 AM   #3
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Hi. I can't see how (A+I)B = I makes computation of (A+I)^(-1) cheaper. How do i exploit that that A^(-1) is known?

Thanks in advance
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