Abstract
In this paper we develop two resultant based methods for the computation of the Greatest Common Divisor (GCD) of two polynomials. Let S be the resultant Sylvester matrix of the two polynomials. We modified matrix S to S *, such that the rows with non-zero elements under the main diagonal, at every column, to be gathered together. We constructed modified versions of the LU and QR procedures which require only the \(\frac{1}{3}\) of floating point operations than the operations performed in the general LU and QR algorithms. Finally, we give a bound for the error matrix which arises if we perform Gaussian elimination with partial pivoting to S *. Both methods are tested for several sets of polynomials and tables summarizing all the achieved results are given.
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References
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© 2005 Springer-Verlag Berlin Heidelberg
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Triantafyllou, D., Mitrouli, M. (2005). Two Resultant Based Methods Computing the Greatest Common Divisor of Two Polynomials. In: Li, Z., Vulkov, L., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2004. Lecture Notes in Computer Science, vol 3401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31852-1_63
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DOI: https://doi.org/10.1007/978-3-540-31852-1_63
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24937-5
Online ISBN: 978-3-540-31852-1
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