Definitions

Fürer's algorithm

Fürer's algorithm is an integer multiplication algorithm for very large numbers possessing a very low asymptotic complexity. It was created in 2007 by Martin Fürer of Pennsylvania State University as an asymptotically less-complex algorithm than its predecessor, the Schönhage-Strassen algorithm published in 1971.

The predecessor to the Fürer algorithm, the Schönhage-Strassen algorithm used fast Fourier transforms to compute integer products in time $O\left(n log n loglog n\right)$, and its authors, Arnold Schönhage and Volker Strassen, also conjectured a lower bound for the problem to be solved by an unknown algorithm as $O\left(n log n\right)$. Fürer's algorithm reduces the gap between these two bounds: it can be used to multiply binary integers of length n in time $n log n 2^\left\{O\left(log^* n\right)\right\}$ (or by a Boolean circuit with that many logic gates), where $log^* n$ represents the iterated logarithm operation. The difference between the $loglog n$ and $2^\left\{log^* n\right\}$ factors in the time bounds of the Schönhage-Strassen algorithm and the Fürer algorithm are so small that Fürer's algorithm would only speed up multiplication operations on "astronomically large numbers".

References

PDF download

Search another word or see Fürer algorithmon Dictionary | Thesaurus |Spanish
Copyright © 2014 Dictionary.com, LLC. All rights reserved.
• Please Login or Sign Up to use the Recent Searches feature
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7033150792121887, "perplexity": 1208.7260645487074}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510272680.42/warc/CC-MAIN-20140728011752-00101-ip-10-146-231-18.ec2.internal.warc.gz"}