@inproceedings{d839e1a938fe4922a20fc4473c76e07d,
title = "Verified error bounds for real solutions of positive-dimensional polynomial systems",
abstract = "In this paper, we propose two algorithms for verifying the existence of real solutions of positive-dimensional polynomial systems. The first one is based on the critical point method and the homotopy continuation method. It targets for verifying the existence of real roots on each connected component of an algebraic variety V ∩ Rn defined by polynomial equations. The second one is based on the low-rank moment matrix completion method and aims for verifying the existence of at least one real roots on V ∩Rn. Combined both algorithms with the verification algorithms for zerodimensional polynomial systems, we are able to find verified real solutions of positive-dimensional polynomial systems very efficiently for a large set of examples.",
keywords = "Error bounds, Positive-dimensional polynomial systems, Real solutions, Verification",
author = "Zhengfeng Yang and Lihong Zhi and Yijun Zhu",
year = "2013",
doi = "10.1145/2465506.2465951",
language = "英语",
isbn = "9781450320597",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
pages = "371--378",
booktitle = "ISSAC 2013 - Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation",
note = "38th International Symposium on Symbolic and Algebraic Computation, ISSAC 2013 ; Conference date: 26-06-2013 Through 29-06-2013",
}