Math.NET Numerics
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Add methods for linear and quadratic programming
Linear and quadratic programming methods are great techniques for minimization problems. Other, more complicated methodologies  such as MPC  can built on top of them fairly easily.
65 votes 
VSLab
I think this is a great project. I am suggesting your library for VSLab (http://www.codeplex.com/vslab). I think that an F# wrapper would be great. Are you interested in contribute with your math library in creating a Matlab like environment? Have a look to the project!
19 votes 
Provide principle component analysis
Extend the linear algebra part with PCA using either Singular Value Decomposition or Eigenvalue Decomposition. Easy implementation, great value!
68 votes 
Investigate Mono.Simd
The upcoming Mono.Simd assembly is nearing release. Using these functions in certain areas could give massive performance gains.
28 votes 
171 votes

24 votes

105 votes

Add row echelon and reduced row echelon form computation
Computing reduced row echelon and row echelon form of a Matrix could be used with Gaussian and GaussJordan elimination techniques.
32 votes 
Add interchange/swap function to Matrix class
Add interchange/swap function to Matrix class which would allow swapping two rows or columns in the matrix (i.e. m.swapRows(2,3)).
2 votes 
Add support for surface interpolation (2D, mesh)
Extend the interpolation methods to support 2D surface interpolation, i.e. on a mesh. See http://community.opensourcedotnet.info/forums/t/565.aspx
46 votes 
Provide extremal values for interpolated splines
Provide extremal points and values and thus also min/max for interpolated splines.
2 votes 
Implement MATLAB's pchip interpolation algorithm
Piecewise Cubic Hermite Interpolating Polynomial
33 votes 
Allow interpolation over complex numbers
Currently interpolation only supports real numbers. Consider also to provide special schemes like Laurent interpolation around the unit circle.
6 votes
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