Determines a given function using Chebyshev polynomials.


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Inputs/Outputs

  • cu32.png number of points —

    number of points is the number of equidistant points in the interval (start,end). The default is 10.

  • cdbl.png start —

    start is the start point of the interval. The default is 0.0.

  • cdbl.png end —

    end is the end point of the interval. The default is 1.0.

  • cu32.png order —

    order is the degree of the Chebyshev approximation. The default is 3.

    The degree is the number of different Chebyshev polynomials T0(x), T1(x), …, Tn(x) describing the formula.

  • cstr.png formula —

    formula is a string describing the function under investigation. The formula can contain any number of valid variables.

  • i1ddbl.png C —

    C is an array of coefficients.

    The array of coefficients belongs to T0(x), T1(x), …, Tn(x).

  • i1ddbl.png X —

    X is the x values dividing (start,end) in equidistant subintervals.

  • i1ddbl.png Y —

    Y is the y values of the Chebyshev polynomial at points X.

  • ii32.png error —

    error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

    • For a given natural number n, the following equation approximately represents the function f(x).

    f(x) = c0T0(x) + … + cnTn(x)

    where T0(x), …, Tn(x) are the first Chebyshev polynomials. You can calculate the c0, …, cn as sums of the form

    where for k = 1, ..., n.

    Examples

    Refer to the following example files included with LabVIEW.

    • labview\examples\Mathematics\Optimization\Sequence of Chebyshev Approximations.vi