What is numerical algebraic geometry?

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• 作者：Jonathan D. Hauenstein ^{hauenstein@nd.edu" class="auth_mail" title="E-mail the corresponding author} ; Andrew J. Sommese ^{sommese@nd.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65H10 ; 68W30 ; 14Q99
• 刊名：Journal of Symbolic Computation
• 出版年：2017
• 出版时间：March-April 2017
• 年：2017
• 卷：79
• 期：part_P3
• 页码：499-507
• 全文大小：349 K

文摘

The foundation of algebraic geometry is the solving of systems of polynomial equations. When the equations to be considered are defined over a subfield of the complex numbers, numerical methods can be used to perform algebraic geometric computations forming the area of numerical algebraic geometry. This article provides a short introduction to numerical algebraic geometry with the subsequent articles in this special issue considering three current research topics: solving structured systems, certifying the results of numerical computations, and performing algebraic computations numerically via Macaulay dual spaces.