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visits | member for | 3 years, 5 months |
seen | Sep 1 '12 at 16:40 | |
stats | profile views | 1,391 |
Feb 21 |
awarded | Yearling |
Feb 21 |
awarded | Yearling |
May 4 |
awarded | Necromancer |
Feb 22 |
awarded | Yearling |
Dec 23 |
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Bessel functions in wave propagation and scattering
I'd be cautious while using the built-in routines for high-order Bessel functions. I believe they are computed using recurrence relations (numerically, not symbolically), so there are issues of cancellation. How are you computing the special functions, and how high do you go in n? Ben Adcock points you to a good reference. |
Dec 21 |
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Interesting Applications of the Classical Stokes Theorem?
Daniel, thank you for the reference! |
Dec 21 |
answered | Interesting Applications of the Classical Stokes Theorem? |
Dec 21 |
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Interesting Applications of the Classical Stokes Theorem?
This is a wonderful example! |
Nov 29 |
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Need help to find an efficient algorithm for the following problem!
@Gilead, thanks - of course, you are correct. The constraint that the solution consist of integers renders it (very) hard. I think Xiao-wen Chang has some papers in this area, including one on box-constrained integer least squares: cs.mcgill.ca/~chang/pub/ChaH08.pdf |
Nov 28 |
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Need help to find an efficient algorithm for the following problem!
I suggest rephrasing this as locating the minimizer of $x^T A x - bx +c$, and then using the fact that $A$ is symmetric, and positive semi-definite, to use a Krylov method to solve the associate linear problem. |
Nov 25 |
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Boundary regularity for the Dirichlet problem
Marius Mitrea has a bunch of papers on the regularity of the Dirichlet problem on manifolds. |
Nov 18 |
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Is there some algorithms for solving non-linear matrix equations?
Is there any additional information you can provide on this problem (in terms of $A,B,C,D.E,F$) - is there any reason to expect unique solutions for this system? Trivially, one would interpret this question as a system of $N^2$ equations for the entries of the $N\times N$ matrix $X$. One could then use a host of algorithms including the family of Newton methods. Which algorithm to use will depend on the structure of the equations. |
Nov 6 |
answered | Eigenvalues of Krylov matrices |
Oct 29 |
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How to do (m)Gram-Schmidt orthogonalization with integers ? (real life problem) (“mathematicalized reformulation”)
The matrix appears nearly rank deficient, so I'd suggest using methods for rank-deficient QR decompositions with column pivoting. The key would be Householder/Givens rotations rather than projections. As Igor suggests, Golub and van Loan's book has lots on the numerical analysis of this. Demmel's book will point you to algorithms for your particular situation. |
Oct 28 |
answered | Textbooks for PDE between Strauss and Folland |
Oct 28 |
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How to do (m)Gram-Schmidt orthogonalization with integers ? (real life problem) (“mathematicalized reformulation”)
How are you computing the orthogonal vectors? Pure Gram-Schmidt is the obvious incorrect choice; have you tried using Householder reflections? Those are going to be stabler for a given precision than standard Gram-Schmidt when columns are near-orthogonal. Trefethen and Bau's book would be a good place to look, and Demmel's book would have a comprehensive collection of algorithms for specific situations. |
Oct 25 |
awarded | Nice Answer |
Oct 25 |
revised |
What items MUST appear on a mathematician's CV?
added 305 characters in body |
Oct 25 |
answered | What items MUST appear on a mathematician's CV? |
Oct 20 |
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Simple system of ODEs with periodic coefficients
Mcandril, algori's solution tells you a lot. For example, if $k=0$, your matrix $A(t)$ is constant in time; the solution has simple features. If $k\not=0$, there are three regimes to consider: $|k|\approx 0$, $|k|\rightarrow +\infty$, and the intermediate regimes. The solution in the asymptotic regimes can, and should, be analysed asymptotically (see, eg. Bender and Orszag for inspiration). Also, a word of caution re numerical simulations for large $k$: are you sure you don't have a very stiff ODE system (large separation of time scales)? Did you use a DAE solver? |