منابع مشابه
Estimation of polynomial roots by continued fractions
One of the ways to describe dynamical characteristics of the system is the s-transfer function, which belongs to the class of the so-called external descriptions and from the mathematical point of view it represents a rational function. Decomposition into the partial fractions (sum of exponential functions in the time domain) is based on the knowledge of the roots of the polynomial defined by t...
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cc Is wdF krxwn that, 3n the treginning of the 19th century the mathematicians proved the impossibility ing algebraieaJly polynomial equations of gra?wr than four and as a result their attention d on numerical methods. During this period r conceived the idea to proceed in two steps; that is, first to isolate the roots and then to approximate them to any desired degree of accuracy. Ap proximatio...
متن کاملUnivariate Polynomial Real Root Isolation: Continued Fractions Revisited
We present algorithmic, complexity and implementation results concerning real root isolation of integer univariate polynomials using the continued fraction expansion of real algebraic numbers. One motivation is to explain the method’s good performance in practice. We improve the previously known bound by a factor of dτ , where d is the polynomial degree and τ bounds the coefficient bitsize, thu...
متن کاملGeneralized Continued Logarithms and Related Continued Fractions
We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base b. We show that all of our so-called type III continued logarithms converge and all rational numbers have fin...
متن کاملContinued Logarithms and Associated Continued Fractions
We investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical experimentation we discover that, for one such for...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2002
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa103-4-3