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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
Tom Dickens's user avatar
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1 vote
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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 …
Tom Dickens's user avatar
  • 1,077
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 …
Tom Dickens's user avatar
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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 …
Tom Dickens's user avatar
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