Everything about Multiplication algorithm

🧭 Start here: a 6-step reading path

1. Read the overview: Multiplication algorithmA 5-minute orientation
2. Skim a recent paper: Discovering faster matrix multiplication algorithms with reinforcement learningInfluential work since 2022
3. Pick up a classic book: Multiple Access CommunicationsThe most-reprinted book on the subject
4. Read the landmark paper: A Two's Complement Parallel Array Multiplication AlgorithmCited 502 times
5. Go sideways: Karatsuba algorithmA closely related topic
6. Go sideways: Schönhage–Strassen algorithmA closely related topic

🏆 Landmark papers (most cited)

• A Two's Complement Parallel Array Multiplication Algorithm

  C.R. Baugh, B.A. Wooley · 1973 · IEEE Transactions on Computers · 502 citations

• Hardware implementation of Montgomery's modular multiplication algorithm

  S.E. Eldridge, C.D. Walter · 1993 · IEEE Transactions on Computers · 162 citations

• An RNS Montgomery modular multiplication algorithm

  J.-C. Bajard, L.-S. Didier, P. Kornerup · 1998 · IEEE Transactions on Computers · 113 citations

• Multiplication-free iterative algorithm for LS problem

  Y.V. Zakharov, T.C. Tozer · 2004 · Electronics Letters · 113 citations

• A Hardware Algorithm for Modular Multiplication/Division

  M.E. Kaihara, N. Takagi · 2005 · IEEE Transactions on Computers · 44 citations

• SUMMA: scalable universal matrix multiplication algorithm

  R. A. Van De Geijn, J. Watts · 1997 · Concurrency: Practice and Experience · 39 citations

• Multiplication algorithm in a finite field and tensor rank of the multiplication

  S. Ballet, R. Rolland · 2004 · Journal of Algebra · 33 citations

• A faster modular multiplication algorithm

  Stephen E. Eldridge · 1991 · International Journal of Computer Mathematics · 23 citations

🆕 Influential since 2022

• Discovering faster matrix multiplication algorithms with reinforcement learning

  Alhussein Fawzi, Matej Balog, Aja Huang · 2022 · Nature · 477 citations

• An Iterative Montgomery Modular Multiplication Algorithm With Low Area-Time Product

  Bo Zhang, Zeming Cheng, Massoud Pedram · 2023 · IEEE Transactions on Computers · 24 citations

• Signature based Merkle Hash Multiplication algorithm to secure the communication in IoT devices

  Swati Kumari, Maninder Singh, Raman Singh · 2022 · Knowledge-Based Systems · 22 citations

• A Novel Parallel Algorithm for Sparse Tensor Matrix Chain Multiplication via TCU-Acceleration

  Haotian Wang, Wangdong Yang, Rong Hu · 2023 · IEEE Transactions on Parallel and Distributed Systems · 18 citations

• Area-Efficient Barrett Modular Multiplication With Optimized Karatsuba Algorithm

  Bo Zhang, Shoumeng Yan · 2024 · IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems · 17 citations

📚 Books worth reading

• Multiple Access CommunicationsBoris Bellalta · 2010
• Evolutionary multi-criterion optimizationCarlos M. Fonseca, Kalyanmoy Deb · 2003
• Multiobjective scheduling by genetic algorithmsTapan P. Bagchi · 1999
• Multiobjective Genetic Algorithms for ClusteringUjjwal Maulik · 2011
• 📕Algorithms for multiple imputation and posterior simulation from incomplete multivariate data with ignorable nonresponseJoseph Louis Schafer · 1991
• 📕Zadacha ob optimalʹnom vybore kompleksov tekhnicheskikh sredstv dl͡ia resheni͡ia zadannogo nabora funk͡tsionalʹnykh zadachO. V. Kitova · 1988
• 📕Fatigue and multiple sclerosis · 1998
• Algorithms for Nonlinear Programming and Multiple-Objective DecisionsBerc Rustem · 1998

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

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• Arnold Schönhage Arnold Schönhage (born 1 December 1934 in Lockhausen, now Bad Salzuflen) is a German mathematician and computer scientist. Schönhage was professor at the…
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