Problem with a convolution algorithm

In summary, the conversation discusses a problem with Algorithm 1.26 from "Statistical Mechanics Algorithms and Computations". The person is having trouble understanding the sequence of weights used in the algorithm and asks for clarification. The link to the book is not accessible, but a PDF is provided. The weights are determined by the trapezoidal method of numerical integration and do not directly relate to the underlying problem. The person expresses frustration with the book's explanation.
  • #1
Uriel
16
0
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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  • #2
Link is blocked to outsiders.
 
  • #3
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)
 
  • #4
The weights are just those used by the trapezoidal method of numerical integration. It has nothing to do with the underlying problem.
 
  • #5
Well it certainly isn't a great book when it comes to explain things.

Thank you very much
 

1. What is a convolution algorithm?

A convolution algorithm is a mathematical process used to combine two functions to produce a third function. It is commonly used in signal processing, image processing, and other areas of science and engineering.

2. What are the common problems associated with convolution algorithms?

Some common problems with convolution algorithms include issues with accuracy and efficiency. Inaccuracies can arise from rounding errors or limitations in the precision of the data being processed. Efficiency can be affected by the computational complexity of the algorithm, which can impact the speed and resources required for the process.

3. How can I improve the accuracy of a convolution algorithm?

Improving the accuracy of a convolution algorithm can be achieved by using higher precision data, implementing error correction techniques, or refining the algorithm itself. Additionally, using a larger sample size or smoothing the data can also help improve accuracy.

4. Are there any alternatives to using a convolution algorithm?

Yes, there are alternative methods to performing convolutions, such as using fast Fourier transforms or other mathematical techniques. However, convolution algorithms are still commonly used due to their versatility and applicability to various types of data.

5. How can I optimize the efficiency of a convolution algorithm?

To optimize the efficiency of a convolution algorithm, one can use parallel processing techniques, choose a more efficient algorithm, or optimize the code by reducing unnecessary calculations. Additionally, using specialized hardware or optimizing the data input can also help improve efficiency.

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