Real zeros of the zero-dimensional parametric piecewise algebraic variety

DOI10.1007/s11425-008-0141-9zbMath1177.14096OpenAlexW2064443887MaRDI QIDQ1041521

Yisheng Lai, Ren-Hong Wang, Jinming Wu

Publication date: 2 December 2009

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-008-0141-9

Mathematics Subject Classification ID

Numerical computation using splines (65D07) Numerical smoothing, curve fitting (65D10) Computational aspects of algebraic surfaces (14Q10) Semialgebraic sets and related spaces (14P10) Spline approximation (41A15) Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (9)

The Viro method for construction of Bernstein-Bézier algebraic hypersurface piece ⋮ Bounds on the number of solutions of polynomial systems and the Betti numbers of real piecewise algebraic hypersurfaces ⋮ The maximum number and its distribution of singular points for parametric piecewise algebraic curves ⋮ An algorithm for isolating the real solutions of piecewise algebraic curves ⋮ Real root classification of parametric spline functions ⋮ Real intersection points of piecewise algebraic curves ⋮ Solving parametric piecewise polynomial systems ⋮ Isolating the real roots of the piecewise algebraic variety ⋮ The Viro method for construction of \(C^r\) piecewise algebraic hypersurfaces

Uses Software

• QEPCAD
• DISCOVERER

Cites Work

• Lagrange interpolation by bivariate \(C^1\)-splines with optimal approximation order
• A complete algorithm for automated discovering of a class of inequality-type theorems
• Partial cylindrical algebraic decomposition for quantifier elimination
• Decomposing polynomial systems into simple systems
• Computing triangular systems and regular systems
• An algorithm for isolating the real solutions of semi-algebraic systems
• Polynomial algorithms in computer algebra
• A dimension series for multivariate splines
• The Nöther and Riemann-Roch type theorems for piecewise algebraic curve
• Solving parametric polynomial systems
• Algorithms in real algebraic geometry
• Simple CAD construction and its applications
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