A Continued Fraction Algorithm for Approximating All Real Polynomial Roots

1978 ◽  
Vol 51 (2) ◽  
pp. 112 ◽  
Author(s):  
David Rosen ◽  
Jeffrey Shallit
Keyword(s):  
Continued Fraction ◽  
Real Polynomial ◽  
Polynomial Roots ◽  
Fraction Algorithm

scholarly journals A continued fraction algorithm for real algebraic numbers

1972 ◽  
Vol 26 (119) ◽  
pp. 785-785 ◽  
Author(s):  
David G. Cantor ◽  
Paul H. Galyean ◽  
Horst G. Zimmer
Keyword(s):  
Continued Fraction ◽  
Algebraic Numbers ◽  
Fraction Algorithm

scholarly journals Complex Method on Octagonal Number

2020 ◽  
Vol 8 (4S5) ◽  
pp. 11-13
Keyword(s):  
Number Theory ◽  
Continued Fraction ◽  
Complex Method ◽  
Polygonal Numbers ◽  
Fraction Algorithm

In Number theory Study of polygonal numbers is rich in varity. In this paper we establish a Complex Octagonal Number using Continued Fraction algorithm.

A NEW SYMMETRIC TWO-DIMENSIONAL ALGORITHM

2006 ◽  
Vol 02 (04) ◽  
pp. 489-498
Author(s):  
PEDRO FORTUNY AYUSO ◽  
FRITZ SCHWEIGER
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Dual Graph ◽  
Plane Curve ◽  
Singularity Theory ◽  
Main Topic ◽  
Two Dimensional ◽  
Dimension 2 ◽  
Multidimensional Continued Fraction ◽  
Fraction Algorithm

Continued fractions are deeply related to Singularity Theory, as the computation of the Puiseux exponents of a plane curve from its dual graph clearly shows. Another closely related topic is Euclid's Algorithm for computing the gcd of two integers (see [2] for a detailed overview). In the first section, we describe a subtractive algorithm for computing the gcd of n integers, related to singularities of curves in affine n-space. This gives rise to a multidimensional continued fraction algorithm whose version in dimension 2 is the main topic of the paper.

scholarly journals The length of the continued fraction expansion for a class of rational functions in

1991 ◽  
Vol 34 (1) ◽  
pp. 7-17 ◽  
Author(s):  
Arnold Knopfmacher
Keyword(s):  
Finite Field ◽  
Continued Fraction ◽  
Rational Functions ◽  
Euclidean Algorithm ◽  
Continued Fraction Expansion ◽  
Partial Quotients ◽  
Fraction Algorithm

A study is made of the length L(h, k) of the continued fraction algorithm for h/k where h and k are co-prime polynomials in a finite field. In addition we investigate the sum of the degrees of the partial quotients in this expansion for h/k, h, k in . The above continued fraction is determined by means of the Euclidean algorithm for the polynomials h, k in .

scholarly journals Continued fraction algorithm for Sturmian colorings of trees

2017 ◽  
Vol 39 (9) ◽  
pp. 2541-2569
Author(s):  
DONG HAN KIM ◽  
SEONHEE LIM
Keyword(s):  
Continued Fraction ◽  
Vertex Coloring ◽  
Regular Tree ◽  
Sturmian Words ◽  
Number Of Classes ◽  
Fraction Algorithm

Factor complexity $b_{n}(\unicode[STIX]{x1D719})$ for a vertex coloring $\unicode[STIX]{x1D719}$ of a regular tree is the number of classes of $n$-balls up to color-preserving automorphisms. Sturmian colorings are colorings of minimal unbounded factor complexity $b_{n}(\unicode[STIX]{x1D719})=n+2$. In this article, we prove an induction algorithm for Sturmian colorings using colored balls in a way analogous to the continued fraction algorithm for Sturmian words. Furthermore, we characterize Sturmian colorings in terms of the data appearing in the induction algorithm.

A continued fraction algorithm

1981 ◽  
Vol 37 (1) ◽  
pp. 149-156 ◽  
Author(s):  
P. Van der Cruyssen
Keyword(s):  
Continued Fraction ◽  
Fraction Algorithm
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