A method to compute the determinant of a tri-diagonal matrix

Document Type : Research Paper

Author

Department of Basic Science Engineering, University of Tehran

Abstract

In this paper we first explain a recursive method and then two algorithms to find determinant of a particular state of tri diagonal $ n\times n$ matrices, so that by using them we can obtain determinant without calculation it in the usual manner and in some cases in easier manner. In the first approach by the aid of tri diagonal matrices of smaller sizes, the determinant of the matrix can be calculated recursively. In the first algorithm we place series of $2\times2$ blocks on the main diagonal of the matrix, during the process which has been explained in the article, we get the determinant of that matrix. In second algorithm by the aid of two tables in which their elements obtained by special algorithms, we calculate determinant of the matrix.
 

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References

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History

  • Receive Date: 20 August 2013
  • Revise Date: 15 November 2013
  • Accept Date: 12 November 2013
  • Publish Date: 21 May 2016

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