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Using an Efficient Sparse Minor Expansion Algorithm to Compute Polynomial Subresultants and the Greatest Common Denominator
October 1978 (vol. 27 no. 10)
pp. 945-950
M.L. Griss, Department of Computer Science, University of Utah
In this paper, the use of an efficient sparse minor expansion method to directly compute the subresultants needed for the greatest common denominator (GCD) of two polynomials is described. The sparse minor expansion method (applied either to Sylvester's or Bezout's matrix) naturally computes the coefficients of the subresultants in the order corresponding to a polynomial remainder sequence (PRS), avoiding wasteful recomputation as much as possible. It is suggested that this is an efficient method to compute the resultant and GCD of sparse polynomials.
Index Terms:
sparse polynomials, Inners, minor expansion, polynomial GCD, subresultants, sparse matrices
Citation:
M.L. Griss, "Using an Efficient Sparse Minor Expansion Algorithm to Compute Polynomial Subresultants and the Greatest Common Denominator," IEEE Transactions on Computers, vol. 27, no. 10, pp. 945-950, Oct. 1978, doi:10.1109/TC.1978.1674974
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