| T.R | Title | User | Personal
Name | Date | Lines |
|---|
| 1760.1 | Overdetermined. | CADSYS::COOPER | Topher Cooper | Thu May 27 1993 16:45 | 11 |
| > offcourse the solution is not unique.
My linear algebra is rusty and never was too great, but it sems to me
that you have N� equations (one for each element of A) and 2*N unknowns
(one for each element of u and one for each element of v) so for N
greater than 2 you've got in general an overdetermined problem, not an
underdetermined one. I.e., for most A there will be no solution.
Maple can probably be coaxed into finding solutions when there are any.
Topher
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| 1760.2 | you're both right | AUSSIE::GARSON | nouveau pauvre | Thu May 27 1993 18:39 | 14 |
| re .0
Just off the top of my head, a solution exists iff each row of the
matrix is a (real) multiple of the first row that is not all zeros,
in which case the solution is non-unique and takes the form
u = t * (a column giving the multiples)
v = 1/t * (the first row that is not all zeros)
where t is an arbitrary non-zero real number.
[The special case where the matrix is entirely zeros, not covered by the
above, has obvious solutions and many of them.]
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| 1760.3 | SVD will test for this | GAUSS::ROTH | Geometry is the real life! | Thu May 27 1993 18:39 | 16 |
| I assume you mean the matrix is the outer product of the vectors.
A[i,j] = u[i]*v[j]
The criteria for this is for A to be rank 1, since all rows or
columns are scalar multiples of each other.
The most numerically reliable way to get this would be based
on a singular value decomposition since this would also indicate
just how close A is to really satisfying this criteria.
SVD routines are available in most linear algebra packages, and
I have a copies of these. (See Numerical Recipes for another one;
the latest edition fixes some bugs in the first edition.)
- Jim
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| 1760.4 | | GAUSS::ROTH | Geometry is the real life! | Thu May 27 1993 18:45 | 7 |
| By the way, if the matrix *really* is rank 1, then you could simply
normalize each row or column to be a unit vector.
Then the norms will form one of your vectors (up to sign) and
one of the unit vectors will form the other.
- Jim
|