chebyspace (Chebyshev Node Spacing)

Create a Chebyshev node spaced vector of n points between a and b.

In numerical analysis, Chebyshev nodes are a set of specific real algebraic numbers, used as nodes for polynomial interpolation. They are the projection of equispaced points on the unit circle onto the real interval [−1,1], the diameter of the circle.

For a given positive integer, n, the Chebyshev nodes of the second kind in the closed interval [a,b] are found from:

This will produce behavior similar to that of the built-in MATLAB routine linspace.

To call this routine from your MATLAB session, simply provide the upper and lower bounds as well as the number of points to be used for the chebyshev nodes:

x = chebyspace(-1,+1,5)'

which provides the following output:

x =

                        -1
        -0.707106781186547
      6.12323399573677e-17
         0.707106781186548
                         1