What is the use of the convolution theorem in multiplying large numbers?

In summary, The conversation discussed the potential use of the convolution theorem for multiplying large numbers, specifically in relation to polynomial multiplication. However, it was noted that this method may not provide much efficiency advantage and may not take into account the carry part of the operation. Additionally, the Wikipedia article on Fourier analysis was mentioned, along with its potential applications in prime number searches, particularly through the Great Internet Mersenne Prime Search. However, it was also acknowledged that there may be other methods that are more effective, such as number theoretic transforms which can avoid rounding errors.
  • #1
John Creighto
495
2
I had this dumb though the other day. I can't help wonder if there would ever be a reason to use the convolution theorem to multiply large numbers. It is used to multiply polynomials. But you would need an awful lot of digits to get any efficiency advantages from it and it would not take care of the carry part of the operation.
 
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  • #3
HallsofIvy said:
You might also want to look at this Wikipedia article:
http://en.wikipedia.org/wiki/Fourier_analysis

Okay, interesting. It seems that they use something like it for a prime number search.

http://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_Search

However, there are perhaps superior methods since number theoretic transforms avoid rounding errors:
http://en.wikipedia.org/wiki/Multiplication_algorithm#Fourier_transform_methods
 

Related to What is the use of the convolution theorem in multiplying large numbers?

1. How do I multiply large numbers?

Multiplying large numbers requires the use of the standard multiplication algorithm, also known as the "long multiplication" method. This involves breaking down the numbers into smaller parts and multiplying them one by one, then adding the results together. There are also other methods, such as using a calculator or a computer program, that can be used to multiply large numbers.

2. What is the best way to approach multiplying large numbers?

The best way to approach multiplying large numbers is to break them down into smaller, more manageable parts. This can be done by using the standard multiplication algorithm or by using other methods, such as the grid method or the lattice method. It is also important to have a good understanding of basic multiplication and place value in order to effectively multiply large numbers.

3. Can I use a calculator to multiply large numbers?

Yes, calculators can be used to multiply large numbers as they are designed to handle calculations with many digits. However, it is still important to have a basic understanding of multiplication and place value in order to use a calculator effectively and verify the accuracy of the results.

4. How do I know if my answer is correct when multiplying large numbers?

You can check the accuracy of your answer by using the standard multiplication algorithm to multiply the numbers again. If your answer matches the one you got originally, then it is most likely correct. You can also use a calculator or a computer program to verify the answer.

5. Are there any tips for multiplying large numbers quickly?

One tip for multiplying large numbers quickly is to use shortcuts or mental math strategies, such as rounding or using known facts. Another tip is to practice and become familiar with the standard multiplication algorithm, as this can help you become more efficient in multiplying large numbers.

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