Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Bates, Daniel J."'
Autor:
Bates, Daniel J., Breiding, Paul, Chen, Tianran, Hauenstein, Jonathan D., Leykin, Anton, Sottile, Frank
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was decisively link
Externí odkaz:
http://arxiv.org/abs/2302.08585
Publikováno v:
Military Operations Research, 2023 Jan 01. 28(3), 31-52.
Externí odkaz:
https://www.jstor.org/stable/27254914
Numerical algebraic geometry provides a number of efficient tools for approximating the solutions of polynomial systems. One such tool is the parameter homotopy, which can be an extremely efficient method to solve numerous polynomial systems that dif
Externí odkaz:
http://arxiv.org/abs/1804.04183
Autor:
Cameron, Karleigh J., Bates, Daniel J.
The problem of geolocation of a transmitter via time difference of arrival (TDOA) and frequency difference of arrival (FDOA) is given as a system of polynomial equations. This allows for the use of homotopy continuation-based methods from numerical a
Externí odkaz:
http://arxiv.org/abs/1712.01916
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation, and model selection. These are all optimization problems, well-known to be challenging due to non-linearity, non-conv
Externí odkaz:
http://arxiv.org/abs/1507.04331
We give a Descartes'-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition is satisfied. This was discovered while developing algorithms and softw
Externí odkaz:
http://arxiv.org/abs/1505.05241
Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes implementations of
Externí odkaz:
http://arxiv.org/abs/1310.3297
Autor:
Bates, Daniel J., Oeding, Luke
By using a result from the numerical algebraic geometry package Bertini we show that (up to high numerical accuracy) a specific set of degree 6 and degree 9 polynomials cut out the secant variety $\sigma_{4}(\mathbb{P}^{2}\times \mathbb{P} ^{2} \time
Externí odkaz:
http://arxiv.org/abs/1009.6181
We use Gale duality for polynomial complete intersections and adapt the proof of the fewnomial bound for positive solutions to obtain the bound (e^4+3) 2^(k choose 2) n^k/4 for the number of non-zero real solutions to a system of n polynomials in n v
Externí odkaz:
http://arxiv.org/abs/0706.4134