y**t
发帖数: 50 | 1 chebyshev quadrature is the guassian quardrature over the
integral [-1,1] with weighting functionW(x)=(1-x^2)^{-1/2}
The abscissas for quardrature n are given by the roots
of the chebyshev polynomial of the 1st kind T_n(x)
and there are formulas about the wights too
some example
n abscissas weights
2 +/-0.7071 1.5708
3 0 1.0472
+/-0.8660 1.0472
4...... | r****y
发帖数: 1437 | 2
For an integral
\int{a, b}{W(x)f(x)}
You can scale it to \int{-1, 1},
when W(x) = 1/sqrt(1-x^2), given N, we can calculate N points
in [-1, 1], get a set like this
x1, w1
x2, w2
...
xi, wi
...
And your integration can be approximated by
summation{i=1, N}{wi*f(xi)}
|
|
