منابع مشابه
Two Algorithms for Root Finding in
We present two algorithms for computing the root, or equivalently the xed point, of a function in exact real arithmetic. The rst algorithm uses the iteration of the expression tree representing the function in real arithmetic based on linear fractional transformations and exact oating point. The second and more general algorithm is based on a trisection of intervals and can be compared with the...
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Introduction. The problem of devising optimal methods for numerically approximating the roots of a polynomial has been of interest for several centuries, and is far from solved. There are numerous recent works on root-finding algorithms and their cost, for example, the work of Jenkins and Traub [JT70], Renegar [Ren87], Schönhage [Sch82], and Shub and Smale [SS85, SS86, Sma85]. This list is far ...
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There has always been a close relationship between mathematics and the sciences (astronomy, chemistry, engineering, physics, etc.). When applying mathematics to study some physical phenomenon, it is often the case that we arrive at a mathematical model (an equation or set of equations) of the phenomenon that cannot be conveniently solved with exact formulas. The following classical example from...
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In this paper, we rst show that there are several equivalent keys for t + 1 chosen plaintexts if the degree of the reduced cipher is t?1. This is against the claim by Jakobsen and Knudsen. We also derive an upper bound on the number of equivalent last round keys for t + 1 chosen plaintexts. We further show an eecient method which nds all the equivalent keys by using Rabin's root nding algorithm...
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Root isolation of univariate polynomials is one of the fundamental problems in computational algebra. It aims to find disjoint regions on the real line or complex plane, each containing a single root of a given polynomial, such that the union of the regions comprises all roots. For root solving over the field of complex numbers, numerical methods are the de facto standard. They are known to be ...
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ژورنال
عنوان ژورنال: Delta Journal of Science
سال: 2016
ISSN: 2735-5306
DOI: 10.21608/djs.2016.139918