how `clenshaw` treats non-real numbers about approxfun.jl HOT 3 CLOSED

Yes clenshaw is linear in x, so this is just evaluation. I guess there should be an ::Complex

On 8 Dec 2014, at 6:26 pm, Gustavo Goretkin [email protected] wrote:

clenshaw tries to take imag of non-real numbers, and breaks evaluation at a complex x into
clenshaw(c,real(x))+im*clenshaw(c,imag(x)). Does this correspond to evaluating the polynomial at a complex point or is it something else?

I am trying to evaluate the polynomial at a Dual number, and I don't think this is the behavior I want.

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I might be misunderstanding what "linear in x" means, but if it is true that
x1*clenshaw(c,x1) + x2* clenshaw(c,x2) == clenshaw(c,w1*x1+w2*x2)
then doesn't that mean that c must describe a linear polynomial going through the origin? I would expect that it is linear in the coefficients c.

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Oh yeah, you’re right… I think the implementation is wrong and needs to be fixed

On 8 Dec 2014, at 6:44 pm, Gustavo Goretkin [email protected] wrote:

I might be misunderstanding what "linear in x" means, but if it is true that
x1_clenshaw(c,x1) + x2_ clenshaw(c,x2) == clenshaw(c,w1_x1+w2_x2)
then doesn't that mean that c must describe a linear polynomial going through the origin? I would expect that it is linear in the coefficients c.

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