Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SHOULD PRUNING BE A PRE-PROCESSOR OF ANY LINEAR SYSTEM?

  • Sen, Syamal K. (Department of Mathematical Sciences, Florida Institute of Technology) ;
  • Ramakrishnan, Suja (Department of Mathematical Sciences, Florida Institute of Technology) ;
  • Agarwal, Ravi P. (Department of Mathematical Sciences, Florida Institute of Technology, Mathematics and Statistics Department, King Fahd University of Petroleum and Minerals) ;
  • Shaykhian, Gholam Ali (National Aeronautics and Space Administration (NASA), Technical Integration Office (ITG), Information Technology (IT) Directorate, Kennedy Space Center)
  • Received : 2011.02.09
  • Accepted : 2011.04.29
  • Published : 2011.09.30
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Abstract

So far as a solution of the given consistent linear system is concerned many numerical methods - both mathematically non-iterative as well as iterative - have been reported in the literature over the last couple of centuries. Most of these methods consider all the equations including linearly dependent ones in the system and obtain a solution whenever it exists. Since linearly dependent equations do not add any new information to a system concerning a solution we have proposed an algorithm that identifies them and prunes them in the process of solving the system. The pruning process does not involve row/column interchanges as in the case of Gauss reduction with partial/complete pivoting. We demonstrate here that the use of pruning as an inbuilt part of our solution process reduces computational and storage complexities and also computational error.

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