numeric::gldata -- weights and
abscissae of Gauss-Legendre quadrature
Introductionnumeric::gldata(n, ..) returns the weights
and the abscissae of the Gauss-Legendre quadrature rule with
n nodes.
Call(s)numeric::gldata(n, digits)
Parametersn |
- | the number of nodes: a positive integer |
digits |
- | the number of decimal digits: a positive integer |
ReturnsA list [b,c] is returned. The lists
b=[b[1],..,b[n]] and c=[c[1],..,c[n]] are
numerical approximations of the weights and abscissae with
digits significant digits.
Side
EffectsThe function uses option
remember. It is not sensitive to the environment variable
DIGITS, because the
numerical working precision is specified by the second argument
digits.
Related
Functionsnumeric::gtdata,
numeric::ncdata,
numeric::quadrature
Detailsdigits. The resulting floating point numbers are correct
to digits decimal places.digits should coincide with
the actual value of DIGITS.n=20,40,80,160 with
digits<=200 are stored internally. They are
returned immediately without any computational costs.numeric::gldata leads to computational costs. For any
further call with the same arguments the data are returned
immediately.
Example
1The following call computes the Gaussian data with the
default precision of DIGITS=10 decimal digits:
>> numeric::gldata(4, DIGITS)
[[0.1739274226, 0.3260725774, 0.3260725774, 0.1739274226],
[0.0694318442, 0.3300094782, 0.6699905218, 0.9305681558]]
Example
2For odd n exact rational data for c[(n+1)/2] and b[(n-1)/2] are returned:
>> DIGITS := 4: numeric::gldata(5, DIGITS)
[[0.1185, 0.2393, 64/225, 0.2393, 0.1185],
[0.04691, 0.2308, 1/2, 0.7692, 0.9531]]
>> delete DIGITS:
Backgroundnumeric::quadrature calls
numeric::gldata to provide the data for Gaussian
quadrature.