A new method is presented for the isolation of the real roots of a given integral, univariate, square-free polynomial P. This method is based on Vincent's theorem and only uses: (i) Descartes' rule of signs, and (ii) transformations of the form x = a1 + 1/x′, x′ = a2 + 1/x″, x̸
Infallible polynomial complex root isolation
β Scribed by George E. Collins, Werner Krandick
- Book ID
- 127399506
- Publisher
- ACM Press
- Year
- 1992
- Tongue
- English
- Weight
- 145 KB
- Category
- Library
- ISBN
- 0897914902
No coin nor oath required. For personal study only.
β¦ Synopsis
International Symposium on Symbolic and Algebraic Computation 92: July 27-29, Berkeley California
π SIMILAR VOLUMES
A method is presented tor isolating and refining the real roots of polynomials with either integer or real algebraic number coefficients. For root isolation the method uses a well-known algorithm that is based on Descartes' rule of signs. However, exact arithmetic is replaced as far as possible by v
This paper, for any constant K, provides an exact formula for the average density of the distribution of the complex roots of equation q z q z 2 0 1 2 n y 1 Γ 4 ny1 Γ 4 ny1 qΠΈΠΈΠΈ q z s K where s a q ib and a and b are sequences of independent identically and normally distributed random variables and