Yep, by using two different bases, one Chebyshev and one ultraspherical
(Gegenbauer) polynomials, differential operators become banded operators, and
can be solved in O(n) time.
On 19 Sep 2014, at 12:14 pm, DumpsterDoofus peter.richter@gmail.com wrote:
Haha, I remember reading
Just pushed an update so that the below is possible, for automatically
approximating a function with a singularity. This seems like the same vein
as what you were suggesting.
Fun(x-exp(x)/sqrt(1-x.^2),JacobiWeightSpace(-.5,-.5))
On Monday, September 15, 2014 8:11:18 PM UTC+10, Gabriel
This is really great idea Sheehan!
I love the idea of Chebfun and extending it to Julia, specially aiming at a
general and powerful PDE solver sounds really good. Certainly it will be
very useful.
Thanks again!!
On Wednesday, September 10, 2014 7:22:36 PM UTC-3, Sheehan Olver wrote:
This
Haha, I remember reading through your paper A fast and well-conditioned
spectral method last year and feeling like my head was spinning
afterwards. I vaguely recall that it views differential equations in
GegenbauerC space, a basis choice which has a bunch of super convenient
properties, all
Here’s a partial list of features in Chebfun not in ApproxFun:
1)Automatic edge detection and domain splitting
The automatic splitting capability of chebfun is definitely really cool,
but it always seemed to me to be a bit more then one would need for most
use cases. That is, if I
I’m in the process of retooling ApproxFun to support general
“FunctionSpace”s, so that one needs to only override a few routines
(points,transform,itransform,diff,…) to get most the features of ApproxFun for
free for othert function spaces (e.g., JacobiSpace for Jacobi polynomials,
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,
This is great!
At this point, what are the major differences in functionality between
ApproxFun and Chebfun?
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
