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• W4287635612 abstract "Abstract This work studies the average complexity of solving structured polynomial systems that are characterised by a low evaluation cost, as opposed to the dense random model previously used. Firstly, we design a continuation algorithm that computes, with high probability, an approximate zero of a polynomial system given only as black-box evaluation program. Secondly, we introduce a universal model of random polynomial systems with prescribed evaluation complexity L . Combining both, we show that we can compute an approximate zero of a random structured polynomial system with n equations of degree at most ${D}$ in n variables with only $operatorname {poly}(n, {D}) L$ operations with high probability. This exceeds the expectations implicit in Smale’s 17th problem." @default.
• W4287635612 created "2022-07-25" @default.
• W4287635612 creator A5029244957 @default.
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• W4287635612 date "2023-01-01" @default.
• W4287635612 modified "2023-10-15" @default.
• W4287635612 title "Rigid continuation paths II. structured polynomial systems" @default.
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• W4287635612 doi "https://doi.org/10.1017/fmp.2023.7" @default.
• W4287635612 hasPublicationYear "2023" @default.
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