SVD of a sperse matrix

nelson · science forum beginner Joined: 28 May 2005 Posts: 10

Hi,
i have a sparse rectangular matrix A and i want to find the principal
direction of $A*A'$ where .' denote the transpose. What are the best
algorithm for a problem of this type? I have found some references about
lanczos methods, are thei reliabel for this problem. I don't want to make
the product A*A' during the algorithm because matrix are of the order
10000*10000000

thank for any advice,
nelson

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Allen McIntosh · science forum beginner Joined: 27 May 2005 Posts: 20

nelson wrote:

Guest · Posted: Sat May 28, 2005 8:21 pm Post subject: Re: SVD of a sperse matrix

You can use an iterative method such as that packaged in Arpack. But
iterate with the symmetric matrix

B = [0 A]
[A' 0]

You need to form matrix B times a given vector in the API. No need to
compute A*A'.

You will converge on the partitioned principal vector

[ x y] with singular value, s. Note that x is the piece you are
after, and s^2 is the eigenvalue of your required matrix. You also get
the direction for A'*A as a bonus - that is y. Reading that book is
good, too!

DTB

Guest · Posted: Sun May 29, 2005 10:17 am Post subject: Re: SVD of a sperse matrix

nelson wrote:

nelson · science forum beginner Joined: 28 May 2005 Posts: 10

Allen McIntosh wrote:

Google