Overview

This book is a guide to concepts and practice in numerical algebraic geometry - the solution of systems of polynomial equations by numerical methods. Through numerous examples, the authors show how to apply the well-received and widely used open-source Bertini software package to compute solutions, including a detailed manual on syntax and usage options. The authors also maintain a complementary web page where readers can find supplementary materials and Bertini input files. Numerically Solving Polynomial Systems with Bertini approaches numerical algebraic geometry from a user's point of view with numerous examples of how Bertini is applicable to polynomial systems. It treats the fundamental task of solving a given polynomial system and describes the latest advances in the field, including algorithms for intersecting and projecting algebraic sets, methods for treating singular sets, the nascent field of real numerical algebraic geometry, and applications to large polynomial systems arising from differential equations. Those who wish to solve polynomial systems can start gently by finding isolated solutions to small systems, advance rapidly to using algorithms for finding positive-dimensional solution sets (curves, surfaces, etc.), and learn how to use parallel computers on large problems. These techniques are of interest to engineers and scientists in fields where polynomial equations arise, including robotics, control theory, economics, physics, numerical PDEs, and computational chemistry.

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9781611972696

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Daniel Bates was a Postdoctoral Fellow at the Institute for Mathematics and its Applications (IMA) before starting as an Assistant Professor of Mathematics at Colorado State University in 2008. Professor Bates is a member of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) and is an active member of the SIAM Activity Group on Algebraic Geometry. Jonathan Hauenstein was a Visiting Assistant Professor at Texas A&M University and Postdoctoral Fellow at the Fields Institute and Institut Mittag-Leffler before starting as an Assistant Professor of Mathematics at North Carolina State University in 2012. Professor Hauenstein is a member of the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM). He is an active member of the SIAM Activity Group on Algebraic Geometry. Andrew Sommese was Full Professor of Mathematics at the University of Notre Dame from 1983 to 2010, and has been Vincent J. and Annamarie Micus Duncan Professor of Mathematics at Notre Dame since 1994. He received an Alfred P. Sloan Fellowship in 1979, the Alexander von Humboldt Research Award for Senior U.S. Scientists in 1993, and became a Fellow of the American Mathematical Society in 2012. He is currently on the editorial boards of Advances in Geometry, the Milan Journal of Mathematics, and the Journal of Algebra and its Applications. Charles Wampler has been employed at the General Motors Research and Development Center in Warren, Michigan since 1985, rising to the rank of Technical Fellow in 2003. He has also been an Adjunct Professor at the University of Notre Dame, first in the Department of Mathematics (2004-2010) and subsequently in the Department of Applied and Computational Mathematics and Statistics. He was named a Fellow of the American Society of Mechanical Engineers (ASME) in 2004 and a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2010. He has been on the editorial boards of the ASME Journal of Mechanical Design and Mechanism and Machine Theory and currently serves on the board of the International Journal of Robotics Research. He is a member of the ASME, IEEE and SIAM.

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