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Cheng Cosine
science forum Guru Wannabe
Joined: 26 May 2005
Posts: 168
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 Posted: Fri Jun 16, 2006 1:31 am Post subject:
? determine major singular pair
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Hi:
The are methods to determine the major eigenpair of a square matrix A,
e.g., power method. But what if one is intereseted in determining the major
singular pair of a rectangular matrix? That is those left and right singular
vectors
corresponding to the first largest singular values and those first largest
singular
values themself. Are there algorithm availabe?
Thanks,
by Cheng Cosine
Jun/15/2k6 NC |
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Cheng Cosine
science forum Guru Wannabe
Joined: 26 May 2005
Posts: 168
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| Posted: Fri Jun 16, 2006 4:31 am Post subject:
Re: ? determine major singular pair
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"Cheng Cosine" <acosine@spamfree.com> wrote in message
news:uRnkg.29137$JW5.1119@southeast.rr.com...
| Quote: | Hi:
The are methods to determine the major eigenpair of a square matrix A,
e.g., power method. But what if one is intereseted in determining the
major
singular pair of a rectangular matrix? That is those left and right
singular vectors
corresponding to the first largest singular values and those first largest
singular
values themself. Are there algorithm availabe?
|
Let's add some more conditions. A straightforward approach is to form
B = A^T*A and C = A*A^T and then one can use those methods for solving
a square matrix's major eigenpair to get singular pair. But this approach
has
a drawback on that when the larger dimension of square matrix A is big, say,
A is N-by-M and N is large, then A*A^T is N-by-N and requires significant
computer memory. Thus, a method does not require explicitly formulate
A*A^T is more desired.
Furthermore, in practice, one could face this situation that the explicit
form
of target rectangular matrix A is unknown. All one has are input vector and
corrresponding output vector: A*x = b, A is N-by-M, x is M-by-1, and b is
N-by-1.
Given one x, a vector b can be obtained, but A is unkwnon. This this case,
how does
one obtain A's singular pair? Or maybe we can star with a simpler case when
A
is a square matrix whose dimension is N-by-N, but entries remain unknown.
Thank,
by Cheng Cosine
Jun/16/2k6 NC |
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Peter Spellucci
science forum Guru
Joined: 29 Apr 2005
Posts: 702
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| Posted: Fri Jun 16, 2006 6:00 pm Post subject:
Re: ? determine major singular pair
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In article <uRnkg.29137$JW5.1119@southeast.rr.com>,
"Cheng Cosine" <acosine@spamfree.com> writes:
| Quote: | Hi:
The are methods to determine the major eigenpair of a square matrix A,
e.g., power method. But what if one is intereseted in determining the major
singular pair of a rectangular matrix? That is those left and right singular
vectors
corresponding to the first largest singular values and those first largest
singular
values themself. Are there algorithm availabe?
Thanks,
by Cheng Cosine
Jun/15/2k6 NC
|
svdpack in http://www.netlib.org
will help. In principle Lanczos applied to A'*A but without operating on A'*A
hth
peter |
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