Polynomial root separation examples
نویسندگان
چکیده
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 کاملPolynomial odes: examples, solutions, properties
ABSTRACT. Let P be a polynomial from R → R and D ∈ R. I will consider the properties of the class of ODEs Y ′ = P (y) ; Y (0) = D and their solutions. The solution space to these ODEs form a proper subspace of the analytic functions with ODEs. They have many interesting algebraic and topological properties. I will present efficient methods for generating the power series solutions to these poly...
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2006
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2006.06.003