I'll add to the partial list, just in case it is useful: a) Algorithm for the convolution of Chebyshev series b) Bivariate rootfinding c) Linearity detection of operators (closely related to (5)) d) Automatic (though a little rough) approximation of functions with singularities e) Remez, cf, least squares, pade polynomial approximation f) Vector calculus g) Field of values algorithm
It may be good to have 3), 4), 6), 7), & b). Not sure if Julia offers any advantage for 2), 5), 8), & c). On Thursday, 11 September 2014 19:43:27 UTC-4, Sheehan Olver wrote: > > > Chebfun is a lot more full featured, and ApproxFun is _very_ rough > around the edges. ApproxFun will probably end up a very different animal > than chebfun: right now the goal is to tackle PDEs on a broader class of > domains, something I think is beyond the scope of Chebfun due to issues > with Matlab's speed, memory management, etc. > > Here’s a partial list of features in Chebfun not in ApproxFun: > > 1) Automatic edge detection and domain splitting > 2) Support for delta functions > 3) Built-in time stepping (pde15s) > 4) Eigenvalue problems > 5) Automatic nonlinear ODE solver > 6) Operator exponential > 7) Smarter constructor for determining convergence > 8) Automatic differentiation > > I have no concrete plans at the moment of adding these features, though > eigenvalue problems and operator exponentials will likely find their way in > at some point. > > > Sheehan > > > On 12 Sep 2014, at 12:14 am, Steven G. Johnson <[email protected] > <javascript:>> wrote: > > > This is great! > > > > At this point, what are the major differences in functionality between > ApproxFun and Chebfun? > >
