A New Parallel Algorithm For Evaluating The Determinant of A Matrix of Order n

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A New Parallel Algorithm For Evaluating The
Determinant of A Matrix of Order n

• H.Teimoori and M.Bayat
• Islamic Azad university of Zanjan,Zanjan ,Iran
• Institute for Advanced Studies in Basic
  Sciences,Zanjan,Iran
• A.Amiri and E.Sarijloo
• Iran university of Sience and Technology
• Islamic Azad university of Zanjan,Zanjan ,Iran

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In This Paper ..

• Present a New Recursive Idea for Evaluation of
  Determinant of Order n
• Design a New Parallel Algorithm based on New
  Method
• The efficiency of New Algorithm
• Pipeline and its effect on Algorithm efficiency

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a New Recursive Idea for Evaluation of
Determinant of Order n

• This approach has been introduced for the first
  time in 5,6
• Before going through the details of methods and
  proof we show how to use this new approach to
  evaluate Determinant of matrix of size 33 and 44

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Determinant of matrix of size 33 and 44 in new
..

• Matrix of size 33

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Determinant of matrix of size 33 and 44 in new
..Cont.

• Matrix of size 44

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General Theorem of New Approach

• Let Maij be a square matrix of order n,then

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New Parallel Algorithm based on New Method

• H.Wa nn Mesh Architecture With CREW Shared
  Memory

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New Parallel Algorithm .Cont.

• In each step Pij must compute the following task

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New Parallel Algorithm .Cont.
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Analysis of Algorithm

• The algorithm has 3 loop
• A sequential loop with order of O(n)
• Two parallel algorithm with order of O(1)
• So the Time Complexity of New Algorithm is O(n)
• For Pipeline approach the algorithm can reach to
  O(nkk) efficiency

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References

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  1985, 63-69.

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• 4 S. J. Berkowitz, On computing the determinant
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• 6 H. Teimoori and M. Bayat, A Recursive method
  for evaluating of determinants, Submitted,(2005).

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• 7 Donald E. Knuth, Overlapping Pfaffians,
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