Flying Flog Consulting have recently published F# for Numerics. Here's how they describe the library:

Our new F# for Numerics library is a suite of numerical methods that leverage functional programming with F#...

This library implements numerical methods from a variety of different disciplines in a uniform way ...:

  • Local and global function minimization and maximization.
  • Mean, median, mode, variance, standard deviation, skew, kurtosis, Shannon entropy and other statistical quantities.
  • Interpolation, curve fitting and regression.
  • Matrix factorizations including eigenvalue computation.
  • Numerical integration and differentiation.
  • Spectral methods including the Fast Fourier Transform.

The first update has reportedly added:

  • FFTs now 2× faster.
  • 1D FFTs over both arrays and vectors.
  • 2D FFTs over F# matrices with parallelism to exploit multicores.
  • Linear, cubic spline and Lagrange polynomial interpolation.
  • More special functions including sinc, the error function and the probit function.
  • Faster Mersenne Twister random number generation, particularly over the Normal distribution.
  • Physical constants.
  • More worked examples.
  • The binomial function for combinatorics.