منابع مشابه
Polynomial Minimum Root Separation
The minimum root separation of an arbitrary polynomial P is defined as the minimum of the distances between distinct (real or complex) roots of P. Some asymptotically good lower bounds for the root separation of P are given, where P may have multiple zeros. There are applications in the analysis of complexity of algorithms and in the theory of algebraic and transcendental numbers.
متن کاملThe Minimum Root Separation of a Polynomial
The minimum root separation of a complex polynomial A is defined as the minimum of the distances between distinct roots of A. For polynomials with Gaussian integer coefficients and no multiple roots, three lower bounds are derived for the root separation. In each case the bound is a function of the degree, n, of A and the sum, d, of the absolute values of the coefficients of A. The notion of a ...
متن کاملAn Algebraic Method for Separating Close-root Clusters and the Minimum Root Separation
Given a univariate polynomial over C, we discuss two issues, an algebraic method for separating a factor of mutually close roots from the polynomial, and a reasonable formula for the minimum root separation, by assuming that the close roots form well-separated clusters. The technique we use is very simple and effective; we move the origin near to the center of a close-root cluster, then we are ...
متن کاملMore Polynomial Root Squeezing
1. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd ed., John Wiley, 1968. 2. R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, 1989. 3. R. Hirshon and R. De Simone, An offer you can’t refuse, Mathematics Magazine 81 (2008) 146–152. 4. L. Takács, On the classical ruin problems, J. American Stat...
متن کاملPolynomial Root Motion
A polynomial is determined by its roots and its leading coefficient. If you set the roots in motion, the critical points will move too. Using only tools from the undergraduate curriculum, we find an inverse square law that determines the velocities of the critical points in terms of the positions and velocities of the roots. As corollaries we get the Polynomial Root Dragging Theorem and the Pol...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2001
ISSN: 0747-7171
DOI: 10.1006/jsco.2001.0481