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• W2279337952 abstract "Homotopy continuation techniques may be usedto approximate all isolated solutions of a polynomial system. Morerecent methods which form the crux of the young field known asnumerical algebraic geometry may be used to produce a descriptionof the complete solution set of a polynomial system, including thepositive-dimensional solution components. There are four maintopics in the present thesis: three novel numerical methods and onenew software package. The first algorithm is a way to increaseprecision as needed during homotopy continuation path tracking inorder to decrease the computational cost of using high precision.The second technique is a new way to compute the scheme structure(including the multiplicity and a bound on the Castelnuovo-Mumfordregularity) of an ideal supported at a single point. The thirdmethod is a new way to approximate all solutions of a certain classof two-point boundary value problems based on homotopycontinuation. Finally, the software package, Bertini, may be usedfor many calculations in numerical algebraic geometry, includingthe three new algorithms described above." @default.
• W2279337952 created "2016-06-24" @default.
• W2279337952 creator A5089126031 @default.
• W2279337952 date "2006-04-07" @default.
• W2279337952 modified "2023-09-26" @default.
• W2279337952 title "Theory and Applications in Numerical Algebraic Geometry" @default.
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• W2279337952 hasPublicationYear "2006" @default.
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