The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Algorithms for exact polynomial root calculation
Algorithms for exact polynomial root calculation
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Symbolic mathematical computation—introduction and overview
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The calculation of multivariate polynomial resultants
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
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This paper discusses a set of algorithms which given a univariate polynomial with integer coefficients (with possible multiple zeros) and a positive rational error bound, uses infinite-precision integer arithmetic and Sturm's Theorem to compute intervals containing the real zeros of the polynomial and whose lengths are less than the given error bound. The algorithms also provide a simple means of determining the number of real zeros in any interval. Theoretical computing time bounds are developed for the algorithms and some empirical results are reported.