The prime-factor algorithm (PFA), also called the Good–Thomas algorithm (1958/1963), is a fast Fourier transform (FFT) algorithm that re-expresses the discrete Fourier transform (DFT) of a size N = N1N2 as a two-dimensional N1×N2 DFT, but only for the case where N1 and N2 are relatively prime. These smaller transforms of size N1 and N2 can then be evaluated by applying PFA recursively or by using some other FFT algorithm. PFA should not be confused with the mixed-radix generalization of the popular Cooley–Tukey algorithm, which also subdivides a DFT of size N = N1N2 into smaller transforms of size N1 and N2. The latter algorithm can use any factors (not necessarily relatively prime), but it has the disadvantage that it also requires extra multiplications by roots of unity called twiddle factors, in addition to the smaller transforms. On the other hand, PFA has the disadvantages that it only works for relatively prime factors (e.g. it is useless for power-of-two sizes) and that it requires more complicated re-indexing of the data based on the additive group isomorphisms. Note, however, that PFA can be combined with mixed-radix Cooley–Tukey, with the former factorizing N into relatively prime components and the latter handling repeated factors. PFA is also closely related to the nested , where the latter performs the decomposed N1 by N2 transform via more sophisticated two-dimensional convolution techniques. Some older papers therefore also call Winograd's algorithm a PFA FFT. (Although the PFA is distinct from the Cooley–Tukey algorithm, Good's 1958 work on the PFA was cited as inspiration by Cooley and Tukey in their 1965 paper, and there was initially some confusion about whether the two algorithms were different. In fact, it was the only prior FFT work cited by them, as they were not then aware of the earlier research by Gauss and others.) (Wikipedia).
Prime Factorization - Fermat Algorithm
Description and example of getting the prime factors of a number using the Fermat algorithm. Questions? Feel free to post them in the comments and I'll do my best to answer!
From playlist Cryptography and Coding Theory
This video explains how to determine the prime factorization of a number using a factor tree. http://mathispower4u.yolasite.com/
From playlist Number Sense - Whole Numbers
Product of Prime Factors GCSE 9-1 Maths
Writing a number as the product of its prime factors index form! An essential skill for higher and foundation GCSE 9-1 maths!
From playlist Prime Numbers, HCF and LCM - GCSE 9-1 Maths
Ex 2: Determine Factors of a Number
This is the second of three videos that provides examples of how to determine the factors of a number using a numbers prime factors. Search Video Library at http://www.mathispower4u.wordpress.com
From playlist Factors and Prime Factorization
Prime Factors | Number | Maths | FuseSchool
Prime Factors | Number | Maths | FuseSchool Every single positive number can be broken down into prime factors. Every single positive number has a unique set of prime factors. It’s the fundamental theorem of arithmetic. Prime factors are used in cryptology to keep data safe. In this video
From playlist MATHS: Numbers
Algebra - Ch. 6: Factoring (4 of 55) What is a Prime Number?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a prime number. A prime number is a positive integer that can only be written as a product of one and itself. Its factors are “1” and itself. To donate: http://www.ilectureonline.com/
From playlist ALGEBRA CH 6 FACTORING
Prime Factoring - GCSE Mathematics Revision (Foundation)
What are prime numbers? Learn how to find the prime factors of a number and write it as a product of prime factors. ❤️ ❤️ ❤️ Support the channel ❤️ ❤️ ❤️ https://www.youtube.com/channel/UCf89Gd0FuNUdWv8FlSS7lqQ/join
From playlist Number
Lec 20 | MIT RES.6-008 Digital Signal Processing, 1975
Lecture 20: Computation of the discrete Fourier transform, part 3 Instructor: Alan V. Oppenheim View the complete course: http://ocw.mit.edu/RES.6-008 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT RES.6-008 Digital Signal Processing, 1975
Jean-Louis Roch - Conférence organisée par l'Institut Fourier et le Laboratoire Jean Kuntzmann
Conférence organisée par l'Institut Fourier et le Laboratoire Jean Kuntzmann Licence: CC BY NC-ND 4.0
From playlist Conférences grand public "MathEnVille"
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/simuleios
From playlist Misc
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/simuleios
From playlist Misc
Example: Determining the Least Common Multiple Using Prime Factorization
This video provides an example of determining the least common multiple of two numbers by using prime factorization. Complete video list at http://www.mathispower4u.com
From playlist Factors, Prime Factors, and Least Common Factors
Still developing my research code: https://github.com/gpue-group/gpue (I'll be uploading regular streams again after domain coloring) -- Watch live at https://www.twitch.tv/simuleios
From playlist research
This video provides an example of how to determine the prime factorization of a whole number. Search Video Library at http://www.mathispower4u.wordpress.com
From playlist Factors and Prime Factorization
Broadcasted live on Twitch -- Watch live at https://www.twitch.tv/simuleios
From playlist Misc
Lec 23 | MIT 18.085 Computational Science and Engineering I
Fast fourier transform and circulant matrices A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007
Fang Song - Introduction to quantum computing Part 2 of 3 - IPAM at UCLA
Recorded 26 July 2022. Fang Song of Portland State University presents "Introduction to quantum computing II" at IPAM's Graduate Summer School Post-quantum and Quantum Cryptography. Abstract: This lecture will focus on two major (families of) quantum algorithms: period finding (a.k.a. Hidd
From playlist 2022 Graduate Summer School on Post-quantum and Quantum Cryptography
The Fast Fourier Transform (FFT): Most Ingenious Algorithm Ever?
In this video, we take a look at one of the most beautiful algorithms ever created: the Fast Fourier Transform (FFT). This is a tricky algorithm to understand so we take a look at it in a context that we are all familiar with: polynomial multiplication. You will see how the core ideas of t
From playlist Fourier
Lecture: Discrete Fourier Transform (DFT) and the Fast Fourier Transform (FFT)
This lecture details the algorithm used for constructing the FFT and DFT representations using efficient computation.
From playlist Beginning Scientific Computing