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 Yearling
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Aug
19
comment Decomposition of a degenerate conic
@Pierluigi: How does one perform this decomposition algorithmically using computer routines? In your other post the lines $l$ and $m$ very much seem to be obtained "by inspection", but how do you do that rigorously?
Jul
28
awarded  Yearling
Jul
2
reviewed Reject Polar Equation area
Jul
2
answered A closed form for the coefficients of Chebyshev polynomials
Jul
2
comment A closed form for the coefficients of Chebyshev polynomials
The Wikipedia page gives some forms, but probably needs a lot of manipulation for what you want. May I ask why you want the monomial coefficients?
Jul
1
answered Uniform Sampling on Intersection of Simplices
Jul
1
comment Orthonormal basis for the null space of almost-Householder matrix
This is not a Householder matrix. A Householder matrix is nonsingular.
Jun
30
comment Uniform Sampling on Intersection of Simplices
I assume you are performing rejection sampling on a transformed space rather than on a bounding box in the actual coordinate space of $x$? You should calculate the maximum volume inscribed ellipsoid and reparameterize in the bounding box of the rotated space (determined by the axes of the ellipsoid). These parameterizations can all be solved with convex programming so they should not be too computationally expensive.
Jun
30
answered Why the Householder matrix is orthogonal?
Jun
30
comment Eigenvalues of an upper Hessenberg matrix
Check out this paper.
Jun
30
comment Eigenvalues of an upper Hessenberg matrix
Check out the MAGMA project that aims to implement linear algebra on the GPU. Edit: MAGMA doesn't support non-symmetric problems. Let me look up this other thing...
Jun
30
comment Eigenvalues of an upper Hessenberg matrix
And I'm sure the Matlab algorithm will take advantage of the fact that it is already upper Hessenberg, since I know that the Lapack code does it.
Jun
30
answered Eigenvalues of an upper Hessenberg matrix
Jun
30
comment Why does this hyperboloid change into a surface?
The correct surface is two parallel planes. I don't know why in one case it would plot only one plane; that may be an artifact of the software you are using.
Jun
30
answered Eigenvalue Deflation (Wielandt or Hotelling)
Jun
30
comment Why does this hyperboloid change into a surface?
Your code for the first expression has a typo; the x*y term appears twice.
Jun
29
answered Delaunay Triangulation on Convex Polytopes — Uniform Sampling
Jun
27
awarded  Tenacious
Jun
27
comment Numerically find a potential field from gradient
Are your points on a grid or are they free-form?
Jun
25
comment Computing the Log-Euclidean distance efficiently by using eigen-analysis.
If you actually know nothing about the eigenstructure of $A$ and $B$, then you can't do any better than the straightforward implementation: compute the two eigendecompositions, perform the logs, reconstitute the products, take the difference, then compute the root-sum-of-squares norm. Attempting to exploit the orthogonal-invariance of the Frobenius norm doesn't gain any advantage here since it just shifts around when you do the matrix multiplications.