- #1
confused_engineer
- 39
- 2
Hello everyone.
I am studying this article since I am interested in optimization. The article makes use of Clenshaw–Curtis quadrature scheme to discretize the integral part of the cost function to a finite sum using Chebyshev polynomials.
The article differentiates between the case of odd and even number of collocation points. In equation 27 and 28 (fourth page), the case of N even is discussed. If N is even, then the N+1 collocation points, including 0, form a vector of odd length.
Then weights are calculated as ws=wN-s=... for s=1, 2, ..., N/2. Meanwhile, w0 and wN are calculated on a different way.
This in turn means that one of the elements is calculated twice, as shown in the following example:
N=6; N+1=7; N/2=3; s=1, 2, 3; N-s=6-1=5, 6-2=4, 6-3=3.
As you can see, the fourth element of the vector, number 3, appears two times. I find this weird. Can someone please tell me if I am understanding the article wrong or if this is intended to happen?
Thanks for reading.
Regards.
I am studying this article since I am interested in optimization. The article makes use of Clenshaw–Curtis quadrature scheme to discretize the integral part of the cost function to a finite sum using Chebyshev polynomials.
The article differentiates between the case of odd and even number of collocation points. In equation 27 and 28 (fourth page), the case of N even is discussed. If N is even, then the N+1 collocation points, including 0, form a vector of odd length.
Then weights are calculated as ws=wN-s=... for s=1, 2, ..., N/2. Meanwhile, w0 and wN are calculated on a different way.
This in turn means that one of the elements is calculated twice, as shown in the following example:
N=6; N+1=7; N/2=3; s=1, 2, 3; N-s=6-1=5, 6-2=4, 6-3=3.
As you can see, the fourth element of the vector, number 3, appears two times. I find this weird. Can someone please tell me if I am understanding the article wrong or if this is intended to happen?
Thanks for reading.
Regards.