File:Bound on matrix multiplication omega over time.svg
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Size of this PNG preview of this SVG file: 380 × 340 pixels. Other resolutions: 268 × 240 pixels | 537 × 480 pixels | 858 × 768 pixels | 1,145 × 1,024 pixels | 2,289 × 2,048 pixels.
Original file (SVG file, nominally 380 × 340 pixels, file size: 51 KB)
Summary
| Description |
English: The bound on the matrix multiplication exponent ω over time. Based on the account given in the introduction of Williams' paper.
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| Date | |
| Source | Own work |
| Author | Self |
| Other versions |
[]
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| SVG development |  This diagram was created with Mathematica. |
| Source code | Mathematica codeplotRange = {{1950, 2015}, {2.32, 3.01}};
data = {{1950, 3}, {1968, 3}, {1969, 2.808}, {1978, 2.796}, {1979, 2.78}, {1980.5, 2.522}, {1981, 2.517}, {1981.5, 2.496}, {1986, 2.479}, {1990, 2.376}, {2010, 2.374}, {2012, 2.373}};
dataPlot = ListPlot[data, Joined -> True, Mesh -> All, PlotRange -> plotRange];
labelData = {{"naive", {1959, 2.985}}, {"Strassen", {1964, 2.825}}, {"Pan", {1976, 2.815}}, {"Bini et al.", {1985.5, 2.78}}, {"Schönhage", {1974, 2.53}}, {"Romani", {1986, 2.52}}, {"Coppersmith-Winograd", {1967.5, 2.49}}, {"Strassen", {1991.3, 2.48}}, {"Coppersmith-Winograd", {1975.5, 2.393}}, {"Stothers", {2005, 2.39}}, {"Williams", {2010, 2.36}}};
labels = Text[#[[1]], #[[2]]] & /@ labelData;
Show[dataPlot, Graphics[{Black, labels}], PlotRange -> plotRange, GridLines -> Automatic, GridLinesStyle -> Directive[Opacity[0.6], Dashed], AxesLabel -> {"Year", "\[Omega]"}, AspectRatio -> 1]
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 22:46, 15 October 2019 | | 380 × 340 (51 KB) | wikimediacommons>A3nm | Add 2014 bound by Le Gall. Edited SVG file directly using Inkscape -- I didn't use Mathematica, so the provided source code is no longer valid. |
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