Title: Chebyshev Approximations

A Chebyshev series is stored using the GSL::Cheb class.

1 Class methods

GSL::Cheb.new(n)

GSL::Cheb.alloc(n)

This create an instance of the GSL::Cheb class for a Chebyshev series of order n.

2 Methods

GSL::Cheb#init(f, a, b)

This computes the Chebyshev approximation the function f over the range (a,b) to the previously specified order. Where f is a GSL::Function object. The computation of the Chebyshev approximation is an O(n^2) process, and requires n function evaluations.

• ex: Approximate a step function defined in (0, 1) by a Chebyshev series of order 40.

  f = GSL::Function.new { |x|
    if x < 0.5
      0.25
    else
      0.75
    end
  }
  
  cs = GSL::Cheb.new(40)
  cs.init(f, 0, 1)

GSL::Cheb#eval(x)

This evaluates the Chebyshev series at a given point x.

GSL::Cheb#eval_n(n, x)

This evaluates the Chebyshev series at a given point x, to (at most) the given order n.

GSL::Cheb#calc_deriv()

GSL::Cheb#deriv()

This computes the derivative of the series, and returns a new GSL::Cheb object which contains the computed derivative. The reciever is not changed.

GSL::Cheb#calc_integ()

GSL::Cheb#integ()

This computes the integral of the series, and returns a new GSL::Cheb object which contains the computed integral coefficients. The reciever is not changed.

See also the example script, samples/cheb.rb.

back