chebnodegen {capn}

Unidimensional Chebyshev nodes

Description

The function generates uni-dimensional chebyshev nodes.

Usage

chebnodegen(n, a, b)

Arguments

n

A number of nodes

a

The lower bound of inverval [a,b]

b

The upper bound of interval [a,b]

Details

A polynomial approximant s_{i} over a bounded interval [a,b] is constructed by:

s_{i} = \frac{b+a}{2} + \frac{b-a}{2}cos (\frac{n - i + 0.5 }{n} \pi ) for i = 1,2,\cdots,n.

More detail explanation can be refered from Miranda and Fackler (2002, p.119).

Value

An array n Chebyshev nodes

References

Miranda, Mario J. and Paul L. Fackler. (2002) Applied Computational Economics and Finance. Cambridge: The MIT Press.

Examples

## 10 Chebyshev nodes in [-1,1]
chebnodegen(10,-1,1)
## 5 Chebyshev nodes in [1,5]
chebnodegen(5,1,5)