Effective alpha theory certification using interval arithmetic: alpha theory over regions

DOI10.1007/978-3-031-64529-7_29MaRDI QIDQ6637824

Kisun Lee

Publication date: 13 November 2024

zbMATH Keywords

Newton's methodinterval arithmeticpolynomial equationsalpha theoryanalytic systemnumerical certification

Mathematics Subject Classification ID

Geometric aspects of numerical algebraic geometry (14Q65)

Cites Work

• Certifying solutions to square systems of polynomial-exponential equations
• Newton-Algorithmen zur Bestimmung von Nullstellen mit Fehlerschranken
• Motivations for an arbitrary precision interval arithmetic and the MPFI library
• Algorithm 921
• MPFR
• Introduction to Interval Analysis
• Interval Methods for Systems of Equations
• Complexity of Bezout's Theorem I: Geometric Aspects
• Effective Certification of Approximate Solutions to Systems of Equations Involving Analytic Functions
• A Generalized Interval LU Decomposition for the Solution of Interval Linear Systems
• Certifying approximate solutions to polynomial systems on Macaulay2
• Computing Galois groups of Fano problems
• Certifying zeros of polynomial systems using interval arithmetic

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