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A Space Efficient Flexible Pivot Selection Approach to Evaluate Determinant and Inverse of a Matrix

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  • Hafsa Athar Jafree
  • Muhammad Imtiaz
  • Syed Inayatullah
  • Fozia Hanif Khan
  • Tajuddin Nizami

Abstract

This paper presents new simple approaches for evaluating determinant and inverse of a matrix. The choice of pivot selection has been kept arbitrary thus they reduce the error while solving an ill conditioned system. Computation of determinant of a matrix has been made more efficient by saving unnecessary data storage and also by reducing the order of the matrix at each iteration, while dictionary notation [1] has been incorporated for computing the matrix inverse thereby saving unnecessary calculations. These algorithms are highly class room oriented, easy to use and implemented by students. By taking the advantage of flexibility in pivot selection, one may easily avoid development of the fractions by most. Unlike the matrix inversion method [2] and [3], the presented algorithms obviate the use of permutations and inverse permutations.

Suggested Citation

  • Hafsa Athar Jafree & Muhammad Imtiaz & Syed Inayatullah & Fozia Hanif Khan & Tajuddin Nizami, 2014. "A Space Efficient Flexible Pivot Selection Approach to Evaluate Determinant and Inverse of a Matrix," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-7, February.
  • Handle: RePEc:plo:pone00:0087219
    DOI: 10.1371/journal.pone.0087219
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    Cited by:

    1. Ignacio Algredo-Badillo & José Julio Conde-Mones & Carlos Arturo Hernández-Gracidas & María Monserrat Morín-Castillo & José Jacobo Oliveros-Oliveros & Claudia Feregrino-Uribe, 2020. "An FPGA-based analysis of trade-offs in the presence of ill-conditioning and different precision levels in computations," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-26, June.

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