Randomization, Relaxation, and Complexity in Polynomial Equation Solving.

Intro -- Contents -- Preface -- Multivariate Ultrametric Root Counting -- A Parallel Endgame -- Efficient Polynomial System Solving by Numerical Methods -- Symmetric Determinantal Representation of Formulas and Weakly Skew Circuits -- Mixed Volume Computation in Solving Polynomial Systems -- A Search for an Optimal Start System for Numerical Homotopy Continuation -- Complex Tropical Localization, and Coamoebas of Complex Algebraic Hypersurfaces -- 1. Introduction -- 2. Preliminaries -- 3. Complex tropical hypersurfaces with a simplex Newton polytope -- 4. Tropical mirror hypersurfaces -- 5. Coamoebas of complex tropical hypersurfaces -- 6. Coamoebas of complex algebraic hypersurfaces -- 7. Examples of complex algebraic plane curves coamoebas -- References -- Randomization, Sums of Squares, Near-Circuits, and Faster Real Root Counting -- Dense Fewnomials -- The Numerical Greatest Common Divisor of Univariate Polynomials.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.