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Real zeroes of polynomials
Collins G. (ed), Loos R., Springer-Verlag New York, Inc., New York, NY, 1983. Type: Book (9780387817767)
Date Reviewed: Jun 1 1985

The authors examine several algorithms for isolating real zeros of polynomials. These algorithms are classified as algebraic, rather than numerical. They compute exactly a sequence of disjoint intervals with rational endpoints, each of which contains exactly one real zero.

One algorithm described is due to Kronecker [1]; it is very simple, but is exponential in n, the degree of the polynomial. Another algorithm is based on Sturm sequences; its use is limited because of growth of the coefficients in the Sturm sequence. An algorithm based on Rolle’s theorem [2] produces a sequence of polynomials with smaller coefficients. A new, modified Uspensky algorithm is introduced. A correctness proof is included, and the algorithm is shown to be faster than the others.

Reviewer:  J. A. Howell Review #: CR109488
1) Kronecker, L.Uber den Zahlbegriff. Crelle J. reine und angew, Mathematik 101 (1887), 337–395.
2) Van der Waerden, B. L.Algebra: vol. 1 (Translated by F. Blum and J. R. Schulenberger), Frederick Ungar Publ. Co., New York, 1970.
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Algorithms (I.1.2 )
 
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