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Some Useful Bounds

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Book cover Computer Algebra

Part of the book series: Computing Supplementa ((COMPUTING,volume 4))

Abstract

Some fundamental inequalities for the following values are listed: the determinant of a matrix, the absolute value of the roots of a polynomial, the coefficients of divisors of polynomials, and the minimal distance between the roots of a polynomial. These inequalities are useful for the analysis of algorithms in various areas of Computer algebra.

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References

  1. Güting, R.: Polynomials with Multiple Zeros. Mathematika 14, 181–196 (1967).

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  2. Mahler, K.: An Inequality for the Discriminant of a Polynomial. Michigan Math. J. 11, 257–262 (1964).

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  3. Marden, M.: The Geometry of the Zeros of a Polynomial in a Complex Variable. Publ. AMS 1949, Math. Surv. 3.

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  4. Mignotte, M.: Some Inequalities about Univariate Polynomials. SYMSAC 1981, 195–199.

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© 1983 Springer-Verlag/Wien

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Mignotte, M. (1983). Some Useful Bounds. In: Buchberger, B., Collins, G.E., Loos, R., Albrecht, R. (eds) Computer Algebra. Computing Supplementa, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7551-4_16

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  • DOI: https://doi.org/10.1007/978-3-7091-7551-4_16

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81776-6

  • Online ISBN: 978-3-7091-7551-4

  • eBook Packages: Springer Book Archive

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