Graduate Problem with a convolution algorithm

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The discussion centers on confusion regarding the weights used in Algorithm 1.26 from "Statistical Mechanics Algorithms and Computations." Specifically, the sequence {1/2l, 1/l,..., 1/l, 1/2l} is questioned for its rationale. It is clarified that these weights correspond to the trapezoidal method of numerical integration, indicating they are standard rather than specific to the algorithm's problem. The book's explanations are criticized for lacking clarity. Overall, the weights serve a fundamental role in numerical integration rather than being unique to the algorithm's context.
Uriel
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Hi.

I've been reading "Statistical Mechanics Algorithms and Computations". And I came to a problem while processing Algorithm 1.26 (I attach a link at the end). I don't get why the weights are the way they are, specially I can't understand the sequence {1/2l,1/l,...,1/l,1/2l}.

Does anyone knows why the weights are those and how would be the sequence?

Thanks in advance

https://books.google.com.mx/books?id=g30SDAAAQBAJ&pg=PA47&lpg=PA47&dq=ran01-convolution&source=bl&ots=3kMGHo026k&sig=NYTpKGJiKJcHFai50vR0cLKw484&hl=en&sa=X&sqi=2&ved=0ahUKEwiF1O7IjMzQAhVJKGMKHdDvDhMQ6AEIGjAA#v=onepage&q=ran01-convolution&f=false
 
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Link is blocked to outsiders.
 
mathman said:
Link is blocked to outsiders.

Pff, can you see this pdf? http://blancopeck.net/Statistics.pdf

The part I'm talking about is on the page 47 of the book (60 of the pdf)
 
The weights are just those used by the trapezoidal method of numerical integration. It has nothing to do with the underlying problem.
 
Well it certainly isn't a great book when it comes to explain things.

Thank you very much
 

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