Gauss-Kronrod Quadrature

Simple Gaussian-Kronrod quadrature formula.

gauss_kronrod(f, a, b, ...)

Arguments

f

function to be integrated.

a, b

end points of the interval.

...

variables to be passed to the function.

Details

Gaussian quadrature of degree 7 with Gauss-Kronrod of degree 15 for error estimation, the quadQK15 procedure in the QUADPACK library.

Value

List of value and relative error.

References

Fausett, L. V. (2007). Applied Numerical Analysis Using Matlab. Second edition, Prentice Hall.

Note

The function needs to be vectorized (though this could easily be changed), but the function does not need to be defined at the end points.

See also

quadgk, romberg

Examples

gauss_kronrod(sin, 0, pi)  #  2.000000000000000 , rel.error: 1.14e-12
#> $value
#> [1] 2
#> 
#> $rel.error
#> [1] 1.139977e-12
#> 
gauss_kronrod(exp, 0, 1)   #  1.718281828459045 , rel.error: 0
#> $value
#> [1] 1.718282
#> 
#> $rel.error
#> [1] 0
#> 
                           #  1.718281828459045 , i.e. exp(1) - 1