Real Root Polynomials and Real Root Preserving Transformations
نویسندگان
چکیده
منابع مشابه
Root Preserving Transformations of Polynomials
Consider the real vector space P2 of all polynomials of degree at most 2. High-school students study the roots of the polynomials in P2, while linear algebra students study linear transformations on P2. Is it possible to bring these two groups together to do some joint research? For example, a linear algebra student chooses a specific linear transformation T : P2 → P2 and asks others to study t...
متن کاملRoot Refinement for Real Polynomials
We consider the problem of approximating all real roots of a square-free polynomial f . Given isolating intervals, our algorithm refines each of them to a width of 2−L or less, that is, each of the roots is approximated to L bits after the binary point. Our method provides a certified answer for arbitrary real polynomials, only considering finite approximations of the polynomial coefficients an...
متن کاملRoot refinement for real polynomials using quadratic interval refinement
We consider the problem of approximating all real roots of a square-free polynomial f with real coefficients. Given isolating intervals for the real roots and an arbitrary positive integer L, the task is to approximate each root to L bits after the binary point. Abbott has proposed the quadratic interval refinement method (QIR for short), which is a variant of Regula Falsi combining the secant ...
متن کاملThe Bernstein Basis and Real Root Isolation
In this mostly expository paper we explain how the Bernstein basis, widely used in computer-aided geometric design, provides an efficient method for real root isolation, using de Casteljau’s algorithm. We discuss the link between this approach and more classical methods for real root isolation. We also present a new improved method for isolating real roots in the Bernstein basis inspired by Rou...
متن کاملOn the Complexity of Real Root Isolation
We introduce a new method to isolate the real roots of a square-free polynomial F = ∑i=0 Aix with real coefficients Ai, where |An| ≥ 1 and |Ai| ≤ 2τ for all i. It is assumed that each coefficient of F can be approximated to any specified error bound. The presented method is exact, complete and deterministic. Due to its similarities to the Descartes method, we also consider it practical and easy...
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: International Journal of Mathematics and Mathematical Sciences
سال: 2021
ISSN: 1687-0425,0161-1712
DOI: 10.1155/2021/5585480