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About 10,000 papers for “Rational function”

Rational function graphs

Oelsner, Charles · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2011

This Demonstration displays the graph of the rational function p(x)/q(x). Adjust the minimum and maximum values for x and y to best view interesting portions of the curve. Asymptotes and holes can also be displayed, and zoom provides a global perspective

Cited by 0

Rational function decomposition

Richard Zippel · 1991

Article Rational function decomposition Share on Author: Richard Zippel Cornell University, Ithaca, NY Cornell University, Ithaca, NYView Profile Authors Info & Claims ISSAC '91: Proceedings of the 1991 international symposium on Symbolic and algebraic computationJune 1991 Pages 1–6https://doi.org/10.1145/120694.120695Online:01 June 1991Publication History 35citation571DownloadsMetricsTotal Citations35Total Downloads571Last 12 Months16Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Cited by 69

Unstable rational function approximation

Philip Parker, Brian D. O. Anderson · International Journal of Control · 1987

The problem is considered of approximating a transfer function with stable and unstable poles by a lower-order transfer function with the same number of unstable poles. A method is suggested and compared with alternative known methods based on Hankel-norm approximation. Examples suggest that no one method always outperforms other methods in terms of minimizing the approximation error.

Cited by 17

Rational approximations of the exponential function at rational points

Kalle Leppälä, Tapani Matala-aho, Topi Törmä · arXiv (Cornell University) · 2016

We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.

Cited by 0Open access

Rational approximations of the exponential function at rational points

Kalle Leppälä, Tapani Matala-aho, Topi Törmä · arXiv (Cornell University) · 2016

We give explicit and asymptotic lower bounds for the quantity $|e^{s/t}-M/N|$ by studying a generalized continued fraction expansion of $e^{s/t}$. In cases $|s|\geq 3$ we improve existing results by extracting a large common factor from the numerators and the denominators of the convergents of that generalized continued fraction.

Cited by 0Open access

ABSTRACT Fast Rational Function Reconstruction ∗

Sara Khodadad · 2008

Let F be a field and let f and g be polynomials in F [t] satisfying deg f> deg g. Recall that on input of f and g the extended Euclidean algorithm computes a sequence of polynomials (si,ti,ri) satisfying sif + tig = ri. Thus for i with gcd(ti,f)=1, we obtain rational functions ri/ti ∈ F (t) satisfying ri/ti ≡ g (mod f). In this paper we modify the fast extended Euclidean algorithm to compute the smallest ri/ti, that is, an ri/ti minimizing deg ri +degti. This means that in an output sensitive modular algorithm when we are recovering rational functions in F (t) from their images modulo f(t) wheref(t) is increasing in degree, we can recover them as soon as the degree of f is large enough and we can do this fast. We have implemented our modified fast Euclidean algorithm for F = Zp, pa word sized prime, in Java. Our fast algorithm beats the ordinary Euclidean algorithm around degree 200. This has application to polynomial gcd computation and linear algebra over Zp(t).

Cited by 0

Rational function approximation in Julia

Driscoll, Tobin A. · Zenodo (CERN European Organization for Nuclear Research) · 2023

This package uses the continuous form of the AAA algorithm to adaptively compute rational approximations of functions on intervals and other domains in the complex plane. For the mathematical description, see https://arxiv.org/abs/2305.03677, which is to appear in SISC.

Cited by 0Open access

Forms over rational function fields

Richard Elman, Nikita A. Karpenko, Alexander Merkurjev · Colloquium Publications - American Mathematical Society/Colloquium Publications · 2008

Cited by 0

Rational Function Functional Networks Based on Function Approximation

Dong Dong Wang, You Jun Chen, Hai Jie Pang · Applied Mechanics and Materials · 2012

In order to solve function approximation, a mathematic model of Rational Function Functional Networks (RFFN) based on approximation was proposed and the learning algorithm for function approximation was presented. This algorithm used the lease square method thought and constructed auxiliary function by Lagrange multiplier method, and the parameters of the rational function functional networks were determined by solving a system of linear equations. Results illustrate the effectiveness of the rational function functional networks in solving approximation problems of the function with a pole.

Cited by 1