Complexity of Bezout's theorem. VII: Distance estimates in the condition metric

DOI10.1007/s10208-007-9018-5zbMath1175.65058OpenAlexW2024090003MaRDI QIDQ1022431

Michael Shub, Carlos Beltran

Publication date: 22 June 2009

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10208-007-9018-5

zbMATH Keywords

systems of polynomial equationscondition number

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Complexity and performance of numerical algorithms (65Y20) Numerical computation of roots of polynomial equations (65H04)

Related Items

Self-convexity and curvature, On the geometry and topology of the solution variety for polynomial system solving, Complexity of path-following methods for the eigenvalue problem, A continuation method to solve polynomial systems and its complexity, Rigid continuation paths II. structured polynomial systems, Fast linear homotopy to find approximate zeros of polynomial systems, Spherical Radon transform and the average of the condition number on certain Schubert subvarieties of a Grassmannian, Geometry of polynomials and root-finding via path-lifting, A numerical algorithm for zero counting. III: Randomization and condition, Complexity of sparse polynomial solving: homotopy on toric varieties and the condition metric, On a problem posed by Steve Smale, The unavoidable condition\dots A report on the book. Book review of: P. Bürgisser and F. Cucker, Condition. The geometry of numerical algorithms, Smale’s 17th problem: Average polynomial time to compute affine and projective solutions, Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems

Cites Work

• Complexity of Bezout's theorem. V: Polynomial time
• Massively parallel computations on many-variable polynomials
• Complexity of Bezout's theorem. III: Condition number and packing
• Smale’s 17th problem: Average polynomial time to compute affine and projective solutions
• Complexity of Bezout's Theorem I: Geometric Aspects
• Solving a Polynomial Equation: Some History and Recent Progress
• On the Efficiency of Newton's Method in Approximating All Zeros of a System of Complex Polynomials
• Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item