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Citation bot (talk | contribs) Alter: journal, pages. Formatted dashes. | Use this bot. Report bugs. | Suggested by Abductive | Category:Wikipedia articles needing clarification from May 2025 | #UCB_Category 346/932 |
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| arxiv=2010.05846
| title = A Refined Laser Method and Faster Matrix Multiplication
| journal=
| volume=3
| doi=10.46298/theoretics.24.21
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The result is even faster on a two-layered cross-wired mesh, where only 2''n''-1 steps are needed.<ref>{{cite journal | last1 = Kak | first1 = S | year = 1988 | title = A two-layered mesh array for matrix multiplication | journal = Parallel Computing | volume = 6 | issue = 3| pages = 383–5 | doi = 10.1016/0167-8191(88)90078-6 | citeseerx = 10.1.1.88.8527 }}</ref> The performance improves further for repeated computations leading to 100% efficiency.<ref>{{cite arXiv |last=Kak |first=S. |date=2014 |title=Efficiency of matrix multiplication on the cross-wired mesh array |class=cs.DC |eprint=1411.3273}}</ref> The cross-wired mesh array may be seen as a special case of a non-planar (i.e. multilayered) processing structure.<ref>{{cite journal | last1 = Kak | first1 = S | year = 1988 | title = Multilayered array computing | journal = Information Sciences | volume = 45 | issue = 3| pages = 347–365 | doi = 10.1016/0020-0255(88)90010-2 | citeseerx = 10.1.1.90.4753 }}</ref>
In a 3D mesh with ''n''<sup>3</sup> processing elements, two matrices can be multiplied in <math>\mathcal{O}(\log n)</math> using the DNS algorithm.<ref>{{cite journal | last1 = Dekel | first1 = Eliezer | last2 = Nassimi | first2 = David | last3 = Sahni | first3 = Sartaj | year = 1981 | title = Parallel Matrix and Graph Algorithms | journal = SIAM Journal on Computing | volume = 10 | issue = 4 | pages=
==See also==
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