Algorithm 493: Zeros of a Real Polynomial [C2]

Jenkins, M. A.

doi:10.1145/355637.355643

Cited by 65 publications

(22 citation statements)

References 2 publications

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“…Instead, ellc uses the rpoly algorithm (Jenkins 1975) followed by "root-polishing" using Laguerre's algorithm (Press et al 1992) to ensure that the correct number of real roots is found and to ensure that they are accurate to within the machine floating-point precision. Given the roots of the quartics in x and y, the remaining task is to identify which combinations of these roots correspond to intersections of the ellipses.…”

Section: Appendix A: the Intersections Of Two Ellipsesmentioning

confidence: 99%

ellc: A fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets

Maxted

2016

A&A

149

117

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Context. Very high quality light curves are now available for thousands of detached eclipsing binary stars and transiting exoplanet systems as a result of surveys for transiting exoplanets and other large-scale photometric surveys. Aims. I have developed a binary star model (ellc) that can be used to analyse the light curves of detached eclipsing binary stars and transiting exoplanet systems that is fast and accurate, and that can include the effects of star spots, Doppler boosting and light-travel time within binaries with eccentric orbits. Methods. The model represents the stars as triaxial ellipsoids. The apparent flux from the binary is calculated using Gauss-Legendre integration over the ellipses that are the projection of these ellipsoids on the sky. The model can also be used to calculate the fluxweighted radial velocity of the stars during an eclipse (Rossiter-McLaghlin effect). The main features of the model have been tested by comparison to observed data and other light curve models. Results. The model is found to be accurate enough to analyse the very high quality photometry that is now available from spacespaced instruments, flexible enough to model a wide range of eclipsing binary stars and extrasolar planetary systems, and fast enough to enable the use of modern Monte Carlo methods for data analysis and model testing.

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Section: Appendix A: the Intersections Of Two Ellipsesmentioning

confidence: 99%

ellc: A fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets

Maxted

2016

A&A

149

117

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“…With relative coefficient magnitudes often spanning more than the 16 digits of precision available in a double, we observed catastrophic loss of precision in the eigensolver. Instead we used Bond's implementation of the well-known Jenkins-Traub root finding method [4] from http://www.crbond.com/download/misc/rpoly.cpp. In addition to complexity of implementation, the need for a sophisticated root finding technique in hs are two arguments in favor of our much simpler method.…”

Section: Synthetic Datamentioning

confidence: 99%

Triangulation made easy

Lindström

2010

2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

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We describe a simple and efficient algorithm for twoview triangulation of 3D points from approximate 2D matches based on minimizing the L 2 reprojection error. Our iterative algorithm improves on the one by Kanatani et al. [5] by ensuring that in each iteration the epipolar constraint is satisfied. In the case where the two cameras are pointed in the same direction, the method provably converges to an optimal solution in exactly two iterations. For more general camera poses, two iterations are sufficient to achieve convergence to machine precision, which we exploit to devise a fast, non-iterative method. The resulting algorithm amounts to little more than solving a quadratic equation, and involves a fixed, small number of simple matrixvector operations and no conditional branches. We demonstrate that the method computes solutions that agree to very high precision with those of Hartley and Sturm's original polynomial method [2], though achieves higher numerical stability and 1-4 orders of magnitude greater speed.

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“…Since we now allow for arbitrary jet masses, the general solution for the leptonic b jet momentum requires solving a 8th-order polynomial, which we solve using the Jenkins-Traub algorithm [47]. Because more than one solution may be possible, we compute the integrand for up to four different solutions and sum the likelihood over these different solutions.…”

Section: Integration Variablesmentioning

confidence: 99%

Precision measurement of the top quark mass in the lepton + jets channel using a matrix element method with Quasi-Monte Carlo integration

Lujan¹

2009

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The measurement uses a matrix element integration method to calculate a tt likelihood, employing a Quasi-Monte Carlo integration, which enables us to take into account effects due to finite detector angular resolution and quark mass effects.We calculate a tt likelihood as a 2-D function of the top pole mass m t and ∆ JES , where ∆ JES parameterizes the uncertainty in our knowledge of the jet energy scale;it is a shift applied to all jet energies in units of the jet-dependent systematic error.By introducing ∆ JES into the likelihood, we can use the information contained in W boson decays to constrain ∆ JES and reduce error due to this uncertainty. We use a neural network discriminant to identify events likely to be background, and apply a cut on the peak value of individual event likelihoods to reduce the effect of badly reconstructed events. This measurement uses a total of 4.3 fb −1 of integrated luminosity, requiring events with a lepton, large E T , and exactly four high-energy jets in the pseudorapidity range |η| < 2.0, of which at least one must be tagged as coming from a b quark. In total, we observe 738 events before and 630 events after 1 applying the likelihood cut, and measure m t = 172.6 ± 0.9 (stat.) ± 0.7 (JES) ± 1.1 (syst.) GeV/c 2 , or m t = 172.6 ± 1.6 (tot.) GeV/c 2 .

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Algorithm 493: Zeros of a Real Polynomial [C2]

Cited by 65 publications

References 2 publications

ellc: A fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets

ellc: A fast, flexible light curve model for detached eclipsing binary stars and transiting exoplanets

Triangulation made easy

Precision measurement of the top quark mass in the lepton + jets channel using a matrix element method with Quasi-Monte Carlo integration

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