Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 GaussianQuadratureError

Source Notebook

Find the error in the Gaussian quadrature approximation of a function’s integral

Contributed by: Paul Abbott (additional contributions by Wolfram Research staff)

ResourceFunction["GaussianQuadratureError"][n,f,a,b]

gives the leading term in the error of the elementary n-point Gaussian quadrature formula for the function f on an interval from a to b.

ResourceFunction["GaussianQuadratureError"][n,f,a,b,prec]

attempts to give a result with prec digits of precision.

Details and Options

The function f may be a pure function or a named function defined using Set or SetDelayed.
The error is given as a function of n, a and b multiplied by an mth derivative of the function f. The size of the error is bounded by the maximum of this expression over the interval from a to b.

Examples

Basic Examples (2) 

The GaussianQuadratureError depends on the 10th integral at an unknown abscissa:

In[1]:=
ResourceFunction["GaussianQuadratureError"][5, f, {1, 10}]
Out[1]=

Use the specified precision:

In[2]:=
ResourceFunction["GaussianQuadratureError"][5, f, {a, 10}, 4]
Out[2]=

Version History

  • 2.0.0 – 06 November 2020
  • 1.0.0 – 20 November 2019

Source Metadata

  • Citation:
    • Kahaner, D., Moler, C., Nash, S., Numerical Methods and Software. Prentice-Hall, 1989.
    • Stoer, J., Bulirsch, R., Introduction to Numerical Analysis, 3rd ed. Springer, 2002.

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