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Aug
22
awarded  Notable Question
Feb
21
awarded  Yearling
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Dec
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comment 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
comment 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
comment Interesting Applications of the Classical Stokes Theorem?
This is a wonderful example!
Nov
29
comment 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
comment 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
comment Boundary regularity for the Dirichlet problem
Marius Mitrea has a bunch of papers on the regularity of the Dirichlet problem on manifolds.
Nov
18
comment 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
comment 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
comment 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?
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Oct
25
answered What items MUST appear on a mathematician's CV?