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• W2023415027 abstract "This paper defines a generalization of Newton’s method to deal with solution paths defined by polynomial homotopies that lead to extremal values. Embedding the solutions in a toric variety leads to explicit scaling relations between coefficients and solutions. Toric Newton is a symbolic-numeric algorithm where the symbolic pre-processing exploits the polyhedral structures. The numerical stage uses the additional variables introduced by the homogenization to scale the components of the solution vectors to the complex unit circle. Toric Newton generates appropriate affine charts and enables one to approximate the magnitude of large solutions of polynomial systems." @default.
• W2023415027 created "2016-06-24" @default.
• W2023415027 creator A5003929128 @default.
• W2023415027 date "2000-05-01" @default.
• W2023415027 modified "2023-10-16" @default.
• W2023415027 title "Toric Newton Method for Polynomial Homotopies" @default.
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• W2023415027 doi "https://doi.org/10.1006/jsco.1999.0296" @default.
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