Solving polynomial systems by polyhedral homotopies

DOI10.11650/twjm/1500407124zbMath0945.65052OpenAlexW1782133069MaRDI QIDQ1809738

Tien-Yien Li

Publication date: 21 September 2000

Published in: Taiwanese Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11650/twjm/1500407124

zbMATH Keywords

computational complexityhomotopy continuationpolynomial systemspolyhedral homotopyroot countingisolated rootsBernshtein theory

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Geometric methods (93B27)

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Computing all nonsingular solutions of cyclic-\(n\) polynomial using polyhedral homotopy continuation methods ⋮ Solving polynomial least squares problems via semidefinite programming relaxations ⋮ Numerical root finding via Cox rings ⋮ Partial Newton-correction method for multiple fixed points of semi-linear differential operators by Legendre-Gauss-Lobatto pseudospectral method ⋮ A new augmented singular transform and its partial Newton-correction method for finding more solutions ⋮ Computing curve intersection by homotopy methods ⋮ Eigenfunction expansion method for multiple solutions of fourth-order ordinary differential equations with cubic polynomial nonlinearity ⋮ A new augmented singular transform and its partial Newton-correction method for finding more solutions to nonvariational quasilinear elliptic PDEs ⋮ Mixed volume computation in parallel ⋮ Determining dimension of the solution component that contains a computed zero of a polynomial system ⋮ A symmetric homotopy and hybrid polynomial system solving method for mixed trigonometric polynomial systems ⋮ Polynomial Homotopy Method for the Sparse Interpolation Problem Part I: Equally Spaced Sampling ⋮ HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method ⋮ Central configurations of the five-body problem with equal masses ⋮ An augmented singular transform and its partial Newton method for finding new solutions

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