[SciPy-user] Structured matrices
Anand Patil
anand@soe.ucsc....
Wed Mar 14 11:06:58 CDT 2007
Nils, Barry,
That matrix is also the covariance of Brownian motion evaluated at times [9, 7, 5, 3, 1]. The inverse matrix bears a strong resemblance to the numerical second derivative operator. This makes sense because the second derivative in x of min(x, \xi) is a delta function concentrated at \xi, but there's probably a more important connection that I don't know about.
Maybe this helps explain the strange results? I found some related refs, but haven't looked at them: http://citeseer.ist.psu.edu/347057.html, http://adsabs.harvard.edu/abs/2003EAEJA.....2001X .
Cheers,
Anand
--------------------------
Nils,
Does this matrix come from a particular application? I'm working on algorithms for the non-negative matrix factorization (NMF). With this matrix as input I'm getting some very strange results. So I'm curious about potential applications.
Cheers!
Barry L. Drake
GA Tech
Nils Wagner wrote: Hi all,
I was wondering if the matrix family (see below) has a special name ?
And/or is there a way to construct this matrix via special matrices
(like Hankel, Toeplitz, etc.) ?
[[ 3. 1.]
[ 1. 1.]]
[[ 5. 3. 1.]
[ 3. 3. 1.]
[ 1. 1. 1.]]
[[ 7. 5. 3. 1.]
[ 5. 5. 3. 1.]
[ 3. 3. 3. 1.]
[ 1. 1. 1. 1.]]
[[ 9. 7. 5. 3. 1.]
[ 7. 7. 5. 3. 1.]
[ 5. 5. 5. 3. 1.]
[ 3. 3. 3. 3. 1.]
[ 1. 1. 1. 1. 1.]]
Nils
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