Results 211 to 220 of about 3,063 (257)

Polynomials with Rational Coefficients Which are Hard to Compute

SIAM Journal on Computing, 1974
We present specific polynomials in \(\mathbb{C}[x]\) with algebraic or rational coefficients which are hard to compute (even though arbitrary complex numbers are allowed as inputs for the computation). Examples are: \(\sum_{\delta = 0}^d e^{2\pi i/2^\delta } x^\delta \), \(\sum_{\delta = 0}^d 2^{2^\delta } x^\delta \).
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Computation of the Galois group of a polynomial with rational coefficients. II

Journal of Mathematical Sciences, 2006
Summary: A new method, which enables us to compute rather efficiently the Galois group of a polynomial over \(\mathbb Q\) or over \(\mathbb Z\), is presented. Reductions of this polynomial with respect to different prime modules are studied, and the information obtained is used for the calculation of the Galois group of the initial polynomial.
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Rational Polynomial Coefficients Modeling and Bias Correction by Using Iterative Polynomial Augmentation

Journal of the Indian Society of Remote Sensing, 2018
In this article, we establish an update procedure for rapid positioning coefficients or rational polynomial coefficients (RPCs) via iterative refinements using polynomial augmentation and reference images. RPCs are widely popular in establishing a ground-to-image relationship without using physical sensor model.
Bhaskar Dubey, B. Kartikeyan, Manthira Moorthi Subbiah   +2 more
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On the Zeros of Linear Differential Polynomials with Small Rational Coefficients

Journal of the London Mathematical Society, 1987
We prove the following: Suppose that f(z) is transcendental and meromorphic of finite order in the plane, and that the linear differential polynomial F(z) is defined by \[ F(z)=f^{(k)}(z)+...+a_ 0(z)f(z) \] and is non-constant, where \(a_{k-1}(z),...,a_ 0(z)\) are rational functions vanishing at infinity. Then \[ N(r,1/(fFF'))=O(\log r) \] implies that
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Rational polynomial coefficients generation for high resolution Ziyuan-3 imagery

2017 IEEE 14th International Conference on Networking, Sensing and Control (ICNSC), 2017
Sensor model is required to build the relationship between the three-dimensional (3D) object space and two-dimensional (2D) image space of high resolution satellite imagery (HRSI). However, each satellite sensor has its own imaging system with different physical sensor model, which increases the difficulty of geometric integration of heterogeneous ...
Zhonghua Hong, Shenyuan Xu, Yun Zhang 0012, Yanling Han, Lijun Xu, Yongjiu Feng   +5 more
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Note on the coefficients of rational Ehrhart quasi-polynomials of Minkowski-sums

Online Journal of Analytic Combinatorics, 2015
By extending former results of Ehrhart, it was shown by Peter McMullen that the number of lattice points in the Minkowski-sum of dilated rational polytopes is a quasipolynomial function in the dilation factors. Here we take a closer look at the coefficients of these quasi-polynomials and show that they are piecewise polynomials themselves and that they
Henk, Martin, Link, Eva
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Generating invariants of hybrid systems via sums-of-squares of polynomials with rational coefficients

Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation, 2012
In this paper we discuss how to generate inequality invariants for continuous dynamical systems involved in hybrid systems. A hybrid symbolic-numeric algorithm is presented to compute inequality invariants of the given systems, by transforming this problem into a parameterized polynomial optimization problem.
Min Wu 0003, Zhengfeng Yang
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Rational solutions of linear difference and q-difference equations with polynomial coefficients

Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the computation of rational solutions of linear integro-differential equations with polynomial coefficients

Journal of Symbolic Computation
The authors propose a ``direct'' algorithm for calculating rational solutions to scalar integro-differential equations with polynomial coefficients. In particular, an algorithm for calculating polynomial solutions previously developed by the authors in [``On polynomial solutions of linear integro-differential equations'', IFAC PapersOnLine 55, No.
Moulay A. Barkatou, Thomas Cluzeau
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A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients

Proceedings of the 2007 international workshop on Symbolic-numeric computation, 2007
In recent years semideffinite programming (SDP) has become the standard technique for computing sum of squares (SOS) decompositions of nonnegative polynomials. Due to the nature of the underlying methods, the solutions are computed numerically, and thus are never exact. In this paper we present a software package for Macaulay 2, which aims at computing
Helfried Peyrl, Pablo A. Parrilo
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