convert array (column vector) to chebfun

[Edgar Avalos]

Hi everyone,

Probably this is simple but can't figure out how to convert a numerical array into a chebfun. Specifically a  nx1 double.  So, if I have a column vector v of n elements, how can I convert this into a chebfun? I would like to be able to do something like:

dom = [-1 1];

vCheb=chebfun(@(x) v); % v is a result from another calculation in matlab.

Domain of v is [-1 1], but discretization is not spectral but just simple equally spaced intervals.

Any idea?

Edgar

[Nick Hale]

Hi Edgar

There are a number of ways, which I list below.

The first uses the 'equi' flag, which tells Chebfun to use a 

certain rational interpolant through the (assumed) equally

spaced data.

The second uses polynomial interpolation through equally

spaced points (which is usually a bad idea).

The third uses cubic splines. The downside here is that 

the interpolant is not global (and convergence will probably

be slower than 'equi' as n increases).

n = 9;

t = linspace(-1,1,n)';

v = 1./(1+25*t.^2);

plot(t, v, '.', 'markersize', 20), hold on

f = chebfun(v, 'equi'); plot(f)

g = chebfun.interp1(t,v); plot(g), 

h = chebfun.spline(t, v); plot(h), 

hold off