Multihomogeneous Newton methods

DOI10.1090/S0025-5718-99-01114-XzbMath0951.65049OpenAlexW1983592997MaRDI QIDQ4955862

Michael Shub, Jean-Pierre Dedieu

Publication date: 22 May 2000

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01114-x

zbMATH Keywords

convergencezerosevaluation mapgeneralized eigenvalue problemsmultihomogeneous analytic functionsmultihomogeneous Newton method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of solutions to systems of equations (65H10) 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)

Related Items

Extended Newton methods for conic inequalities: approximate solutions and the extended Smale \(\alpha\)-theory ⋮ On semilocal convergence analysis for two-step Newton method under generalized Lipschitz conditions in Banach spaces ⋮ A primal-dual formulation for certifiable computations in Schubert calculus ⋮ Symplectic methods for the approximation of the exponential map and the Newton iteration on Riemannian submanifolds ⋮ Kantorovich's theorem on Newton's method under majorant condition in Riemannian manifolds ⋮ Complexity of path-following methods for the eigenvalue problem ⋮ Rigid continuation paths II. structured polynomial systems ⋮ Newton's method for overdetermined systems of equations ⋮ Perturbation theory for homogeneous polynomial eigenvalue problems

Cites Work

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• Complexity of Bezout's theorem. III: Condition number and packing
• A modification of the Neumann-Poincaré method for multiply connected regions
• Complexity of Bezout's Theorem I: Geometric Aspects
• Condition Number Analysis for Sparse Polynomial Systems
• COMPLEXITY AND REAL COMPUTATION: A MANIFESTO
• Complexity of Bezout’s Theorem IV: Probability of Success; Extensions

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