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Numerical algorithms for problems in analysis and algebra, scientific computation
1
vote
Numerical multivariate definite integration
Look up "gaussian integral" on Wikipedia. I think you can handle the absolute value portion by splitting the range, and you will get the integral in terms of $ \det A$. Take a look.
Tom
1
vote
Accepted
For what values of the parameter does this function have an elementary anti-derivative?
Hi,
Your integral is the incomplete beta function, and has elementary expressions when $r$ is equal to an integer or half-integer. For example, you found the value for $r=1/2$, and when $r=3$ it is
…
1
vote
Integral Fredholm equation of the second type
I'm not an expert here but it seems like since the integral is a convolution a Fourier or Laplace-based method could work. Might get you into the Wiener-Hopf technique.
Search for transform-based me …
4
votes
Best Numerical Method for Evaluating a Hilbert transform
There is a very recent paper in Mathematics of Computation,
"Computing the Hilbert transform and its inverse"
Sheehan Olver
Math. Comp. 80 (2011), 1745-1767.
He presents a new algorithm and refer …