Content deleted Content added
→Schoolbook algorithm: typo |
m v2.04 - Fix errors for CW project (Unbalanced quotes in ref name or illegal character.) |
||
Line 3:
In [[theoretical computer science]], an active area of research is determining [[Analysis of algorithms|how quickly]] the operation of [[matrix multiplication]] can be performed. [[Matrix multiplication algorithm]]s are a central subroutine in theoretical and [[numerical algorithm|numerical]] algorithms for [[numerical linear algebra]] and [[optimization]], so finding the right amount of time it should take is of major practical relevance.
Directly applying the mathematical definition of matrix multiplication gives an algorithm that requires {{math|''n''<sup>3</sup>}} [[Field (mathematics)|field]] operations to multiply two {{math|''n'' × ''n''}} matrices over that field ({{math|Θ(''n''<sup>3</sup>)}} in [[big O notation]]). Surprisingly, algorithms exist that provide better running times than this straightforward "schoolbook algorithm". The first to be discovered was [[Strassen algorithm|Strassen's algorithm]], devised by [[Volker Strassen]] in 1969 and often referred to as "fast matrix multiplication".<ref name="strassen69">
{{cite journal
| doi=10.1007/BF02165411
Line 83:
! Year !! Bound on omega !! Authors
|-
| 1969 || 2.8074 || [[Volker Strassen|Strassen]]<ref name="strassen69" />
|-
| 1978 || 2.796 || Pan<ref>
| |||