Multiplication algorithm (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Multiplication algorithm" in English language version.

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14doi.org

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Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Harvey, David; van der Hoeven, Joris; Lecerf, Grégoire (2016). "Even faster integer multiplication". Journal of Complexity. 36: 1–30. arXiv:1407.3360. doi:10.1016/j.jco.2016.03.001. MR 3530637.
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.

archive.org

Charles Babbage, Chapter VIII – Of the Analytical Engine, Larger Numbers Treated, Passages from the Life of a Philosopher, Longman Green, London, 1864; page 125.
Castle, Frank (1900). Workshop Mathematics. London: MacMillan and Co. p. 74.

archives-ouvertes.fr

hal.archives-ouvertes.fr

Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.

arxiv.org

De, A.; Saha, C.; Kurur, P.; Saptharishi, R. (2008). "Fast integer multiplication using modular arithmetic". Proceedings of the 40th annual ACM Symposium on Theory of Computing (STOC). pp. 499–506. arXiv:0801.1416. doi:10.1145/1374376.1374447. ISBN 978-1-60558-047-0. S2CID 3264828.
Harvey, David; van der Hoeven, Joris; Lecerf, Grégoire (2016). "Even faster integer multiplication". Journal of Complexity. 36: 1–30. arXiv:1407.3360. doi:10.1016/j.jco.2016.03.001. MR 3530637.
Covanov, Svyatoslav; Thomé, Emmanuel (2019). "Fast Integer Multiplication Using Generalized Fermat Primes". Math. Comp. 88 (317): 1449–1477. arXiv:1502.02800. doi:10.1090/mcom/3367. S2CID 67790860.
Harvey, D.; van der Hoeven, J. (2019). "Faster integer multiplication using short lattice vectors". The Open Book Series. 2: 293–310. arXiv:1802.07932. doi:10.2140/obs.2019.2.293. S2CID 3464567.

bbc.co.uk

news.bbc.co.uk

Eason, Gary (2000-02-13). "Back to school for parents". BBC News.
Eastaway, Rob (2010-09-10). "Why parents can't do maths today". BBC News.

bbc.co.uk

Eason, Gary (2000-02-13). "Back to school for parents". BBC News.
Eastaway, Rob (2010-09-10). "Why parents can't do maths today". BBC News.

books.google.com

"Reviews", The Civil Engineer and Architect's Journal: 54–55, 1857.
Arora, Sanjeev; Barak, Boaz (2009). Computational Complexity: A Modern Approach. Cambridge University Press. ISBN 978-0-521-42426-4.
von zur Gathen, Joachim; Gerhard, Jürgen (1999), Modern Computer Algebra, Cambridge University Press, pp. 243–244, ISBN 978-0-521-64176-0.

core.ac.uk

Ablayev, F.; Karpinski, M. (2003). "A lower bound for integer multiplication on randomized ordered read-once branching programs" (PDF). Information and Computation. 186 (1): 78–89. doi:10.1016/S0890-5401(03)00118-4.
Duhamel, P.; Vetterli, M. (1990). "Fast Fourier transforms: A tutorial review and a state of the art" (PDF). Signal Processing. 19 (4): 259–299 See Section 4.1. doi:10.1016/0165-1684(90)90158-U.

cut-the-knot.org

Bogomolny, Alexander. "Peasant Multiplication". www.cut-the-knot.org. Retrieved 2017-11-04.

doi.org

Brent, Richard P (March 1978). "A Fortran Multiple-Precision Arithmetic Package". ACM Transactions on Mathematical Software. 4: 57–70. CiteSeerX 10.1.1.117.8425. doi:10.1145/355769.355775. S2CID 8875817.
Holmes, Neville (2003), "Multiplying with quarter squares", The Mathematical Gazette, 87 (509): 296–299, doi:10.1017/S0025557200172778, JSTOR 3621048, S2CID 125040256.
Everett L., Johnson (March 1980), "A Digital Quarter Square Multiplier", IEEE Transactions on Computers, vol. C-29, no. 3, Washington, DC, USA: IEEE Computer Society, pp. 258–261, doi:10.1109/TC.1980.1675558, ISSN 0018-9340, S2CID 24813486
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Schönhage, A.; Strassen, V. (1971). "Schnelle Multiplikation großer Zahlen". Computing. 7 (3–4): 281–292. doi:10.1007/BF02242355. S2CID 9738629.
Fürer, M. (2007). "Faster Integer Multiplication" (PDF). Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, June 11–13, 2007, San Diego, California, USA. pp. 57–66. doi:10.1145/1250790.1250800. ISBN 978-1-59593-631-8. S2CID 8437794.
De, A.; Saha, C.; Kurur, P.; Saptharishi, R. (2008). "Fast integer multiplication using modular arithmetic". Proceedings of the 40th annual ACM Symposium on Theory of Computing (STOC). pp. 499–506. arXiv:0801.1416. doi:10.1145/1374376.1374447. ISBN 978-1-60558-047-0. S2CID 3264828.
Harvey, David; van der Hoeven, Joris; Lecerf, Grégoire (2016). "Even faster integer multiplication". Journal of Complexity. 36: 1–30. arXiv:1407.3360. doi:10.1016/j.jco.2016.03.001. MR 3530637.
Covanov, Svyatoslav; Thomé, Emmanuel (2019). "Fast Integer Multiplication Using Generalized Fermat Primes". Math. Comp. 88 (317): 1449–1477. arXiv:1502.02800. doi:10.1090/mcom/3367. S2CID 67790860.
Harvey, D.; van der Hoeven, J. (2019). "Faster integer multiplication using short lattice vectors". The Open Book Series. 2: 293–310. arXiv:1802.07932. doi:10.2140/obs.2019.2.293. S2CID 3464567.
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Ablayev, F.; Karpinski, M. (2003). "A lower bound for integer multiplication on randomized ordered read-once branching programs" (PDF). Information and Computation. 186 (1): 78–89. doi:10.1016/S0890-5401(03)00118-4.
Duhamel, P.; Vetterli, M. (1990). "Fast Fourier transforms: A tutorial review and a state of the art" (PDF). Signal Processing. 19 (4): 259–299 See Section 4.1. doi:10.1016/0165-1684(90)90158-U.
Johnson, S.G.; Frigo, M. (2007). "A modified split-radix FFT with fewer arithmetic operations" (PDF). IEEE Trans. Signal Process. 55 (1): 111–9 See Section IV. Bibcode:2007ITSP...55..111J. doi:10.1109/TSP.2006.882087. S2CID 14772428.

escholarship.org

McFarland, David (2007), Quarter Tables Revisited: Earlier Tables, Division of Labor in Table Construction, and Later Implementations in Analog Computers, p. 1

fftw.org

Johnson, S.G.; Frigo, M. (2007). "A modified split-radix FFT with fewer arithmetic operations" (PDF). IEEE Trans. Signal Process. 55 (1): 111–9 See Section IV. Bibcode:2007ITSP...55..111J. doi:10.1109/TSP.2006.882087. S2CID 14772428.

harvard.edu

ui.adsabs.harvard.edu

Johnson, S.G.; Frigo, M. (2007). "A modified split-radix FFT with fewer arithmetic operations" (PDF). IEEE Trans. Signal Process. 55 (1): 111–9 See Section IV. Bibcode:2007ITSP...55..111J. doi:10.1109/TSP.2006.882087. S2CID 14772428.

jstor.org

Holmes, Neville (2003), "Multiplying with quarter squares", The Mathematical Gazette, 87 (509): 296–299, doi:10.1017/S0025557200172778, JSTOR 3621048, S2CID 125040256.

koreascience.kr

Corlu, M.S.; Burlbaw, L.M.; Capraro, R.M.; Corlu, M.A.; Han, S. (2010). "The Ottoman Palace School Enderun and the Man with Multiple Talents, Matrakçı Nasuh". Journal of the Korea Society of Mathematical Education Series D: Research in Mathematical Education. 14 (1): 19–31.

mathematische-basteleien.de

"Multiplication". www.mathematische-basteleien.de. Retrieved 2022-03-15.

psu.edu

citeseerx.ist.psu.edu

Brent, Richard P (March 1978). "A Fortran Multiple-Precision Arithmetic Package". ACM Transactions on Mathematical Software. 4: 57–70. CiteSeerX 10.1.1.117.8425. doi:10.1145/355769.355775. S2CID 8875817.

quantamagazine.org

Hartnett, Kevin (2019-04-11). "Mathematicians Discover the Perfect Way to Multiply". Quanta Magazine. Retrieved 2019-05-03.

semanticscholar.org

api.semanticscholar.org

Brent, Richard P (March 1978). "A Fortran Multiple-Precision Arithmetic Package". ACM Transactions on Mathematical Software. 4: 57–70. CiteSeerX 10.1.1.117.8425. doi:10.1145/355769.355775. S2CID 8875817.
Holmes, Neville (2003), "Multiplying with quarter squares", The Mathematical Gazette, 87 (509): 296–299, doi:10.1017/S0025557200172778, JSTOR 3621048, S2CID 125040256.
Everett L., Johnson (March 1980), "A Digital Quarter Square Multiplier", IEEE Transactions on Computers, vol. C-29, no. 3, Washington, DC, USA: IEEE Computer Society, pp. 258–261, doi:10.1109/TC.1980.1675558, ISSN 0018-9340, S2CID 24813486
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Schönhage, A.; Strassen, V. (1971). "Schnelle Multiplikation großer Zahlen". Computing. 7 (3–4): 281–292. doi:10.1007/BF02242355. S2CID 9738629.
Fürer, M. (2007). "Faster Integer Multiplication" (PDF). Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, June 11–13, 2007, San Diego, California, USA. pp. 57–66. doi:10.1145/1250790.1250800. ISBN 978-1-59593-631-8. S2CID 8437794.
De, A.; Saha, C.; Kurur, P.; Saptharishi, R. (2008). "Fast integer multiplication using modular arithmetic". Proceedings of the 40th annual ACM Symposium on Theory of Computing (STOC). pp. 499–506. arXiv:0801.1416. doi:10.1145/1374376.1374447. ISBN 978-1-60558-047-0. S2CID 3264828.
Covanov, Svyatoslav; Thomé, Emmanuel (2019). "Fast Integer Multiplication Using Generalized Fermat Primes". Math. Comp. 88 (317): 1449–1477. arXiv:1502.02800. doi:10.1090/mcom/3367. S2CID 67790860.
Harvey, D.; van der Hoeven, J. (2019). "Faster integer multiplication using short lattice vectors". The Open Book Series. 2: 293–310. arXiv:1802.07932. doi:10.2140/obs.2019.2.293. S2CID 3464567.
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Johnson, S.G.; Frigo, M. (2007). "A modified split-radix FFT with fewer arithmetic operations" (PDF). IEEE Trans. Signal Process. 55 (1): 111–9 See Section IV. Bibcode:2007ITSP...55..111J. doi:10.1109/TSP.2006.882087. S2CID 14772428.

springer.com

link.springer.com

Schönhage, A.; Strassen, V. (1971). "Schnelle Multiplikation großer Zahlen". Computing. 7 (3–4): 281–292. doi:10.1007/BF02242355. S2CID 9738629.

txbobsc.com

Putney, Charles (March 1986). "Fastest 6502 Multiplication Yet". Apple Assembly Line. 6 (6).

uni-muenster.de

ivv5hpp.uni-muenster.de

Fürer, M. (2007). "Faster Integer Multiplication" (PDF). Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, June 11–13, 2007, San Diego, California, USA. pp. 57–66. doi:10.1145/1250790.1250800. ISBN 978-1-59593-631-8. S2CID 8437794.

unsw.edu.au

newsroom.unsw.edu.au

Gilbert, Lachlan (2019-04-04). "Maths whiz solves 48-year-old multiplication problem". UNSW. Retrieved 2019-04-18.

worldcat.org

Everett L., Johnson (March 1980), "A Digital Quarter Square Multiplier", IEEE Transactions on Computers, vol. C-29, no. 3, Washington, DC, USA: IEEE Computer Society, pp. 258–261, doi:10.1109/TC.1980.1675558, ISSN 0018-9340, S2CID 24813486