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Re: Transpose(A)*P*A [message #62831 is a reply to message #62825]

Sat, 11 October 2008 12:42

Craig Markwardt
Messages: 1869
Registered: November 1996

Senior Member

"mapper4u6@gmail.com" <zjwang2u@gmail.com> writes:

> hello,
>
> I have a question about how to improve the computation speed when deal
> with non-linear equation
> A x = l, P is the weight for each
> row, P is M*M
> M*N N*1 M*1
>
> then I have to build normal matrix which is
> Transpose(A)*P*A x = Transpose(A)*P*l
> N*N N*1 N*1
>
> then x can be solved.

I'm going to channel our vice presidential candidate and answer a
different question.

It looks like you are trying to solve a least squares problem. It's
well documented that the normal equation method suffers from accuracy
problems, basically because you are squaring the A matrix, and thus
squaring the errors. Have you tried SVD or QR factorization?
Implemented correctly, the execution times should scale as,
Normal equation ~ N^2 * ( M + N/3)
QR ~ N^2 * (2*M - 2*N/3)
SVD ~ N^2 * (2*M +11*N/3)
On its face, QR factorization will take longer (not more than double
the time though), but it is known to be more stable.

Craig

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Craig B. Markwardt, Ph.D. EMAIL: cbmarkwardt+usenet@gmail.com
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[Message index]

		Re: Transpose(A)PA By: Karlo Janos on Sun, 12 October 2008 04:24
		Re: Transpose(A)PA By: Craig Markwardt on Sat, 11 October 2008 12:42
		Re: Transpose(A)PA By: Vince Hradil on Fri, 10 October 2008 08:03

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