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Thread Subject:
Numbers of Arithmetic Operations To Compute: (x^T)*(A^-1)*x

Subject: Numbers of Arithmetic Operations To Compute: (x^T)*(A^-1)*x

From: Ashley Daly

Date: 18 Feb, 2009 17:09:02

Message: 1 of 1

I'm not sure if anyone here will be able to help with this question, but I thought it was worth a shot.

Let A be a nxn real symmetric positive definite matrix and x not equal to 0 a real nx1 vector. Show how to compute (x^T)*(A^-1)*x in (n^3)/3 + O(n^2) arithmetic operations.

What I tried doing was setting Ax = b, and then finding out what (x^T)*(A^-1)*x is. However, I'm not sure if that is the right thing to do or how that tells me how many operations there are.

I know that we learned that Cholesky requires (n^3)/3 + O(n^2) arithmetic operations, and I'm not even sure of why that is or how you show that.

Does anyone have any ideas? Thank you so much.

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