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On the probability of generating a primitive matrix

来源:必赢线路检测中心   时间:2023-03-07   点击数:

题目:On the probability of generating a primitive matrix

报告人:陈经纬

时间:2023316日(周四)16:00-16:45

地点:腾讯会议

报告人简介:陈经纬,中国科学院重庆绿色智能技术研究院副研究员,法国国家科研中心(CNRS)并行计算实验室(LIP)、加拿大菲尔兹(Fields)研究所访问学者,中科院青年促进会会员,入选中科院“西部之光”计划。主要从事格的理论、算法与应用研究,尤其是与基于格的密码学相关的方向,主持或参与国家重点研发计划、国家自然科学基金、重庆市自然科学基金、贵州省科技支撑计划等科研项目10余项,发表在Math. Comput., Sci. China, ISSAC等期刊或会议上的论文二十余篇。

摘要:Given a k × n integer primitive matrix A (i.e., a matrix can be extended to an n × n unimodular matrix over the integers) with the maximal absolute value of entries A bounded by an integer λ from above, we consider the probability that the m× n matrix extended from A by appending other m − k row vectors of dimension n with entries chosen randomly and independently from the uniform distribution over {0, 1, . . . , λ−1} is still primitive. In this talk, we will report that the probability is at least a constant for fixed m in the range [k+1, n−4]. As an application, we will prove that there exists a fast Las Vegas algorithm that completes a k × n primitive matrix A to an n × n unimodular matrix within expected \tilde{O} (n^ω log A) bit operations, where \tilde{O} is big-O but without log factors, ω is the exponent on the arithmetic operations of matrix multiplication. This talk is based on a joint work with Yong Feng, Yang Liu and Wenyuan Wu.

邀请人:黄巧龙



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