On generalized Newton algorithms: Quadratic convergence, path-following and error analysis

DOI10.1016/0304-3975(94)00065-4zbMath0811.65039OpenAlexW2049823727MaRDI QIDQ1338218

Gregorio Malajovich

Publication date: 7 May 1995

Published in: Theoretical Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-3975(94)00065-4

zbMATH Keywords

complexityNewton's methoderror analysisquadratic convergencepolynomial systemspath-followinghomotopy maps

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) Complexity and performance of numerical algorithms (65Y20)

Related Items

Symplectic methods for the approximation of the exponential map and the Newton iteration on Riemannian submanifolds, Robust certified numerical homotopy tracking, Globally convergent, iterative path-following for algebraic equations, A fast and stable algorithm for splitting polynomials, A numerical algorithm for zero counting. I: Complexity and accuracy, On a transfer theorem for the \(\text{P}\neq \text{NP}\) conjecture, Kronecker's and Newton's approaches to solving: a first comparison, Smale's \(\alpha \)-theory for inexact Newton methods under the \(\gamma \)-condition, On the geometry of Graeffe iteration, Multihomogeneous Newton methods, Newton's method for overdetermined systems of equations, Smale’s 17th problem: Average polynomial time to compute affine and projective solutions, Rigid continuation paths I. Quasilinear average complexity for solving polynomial systems, Some lower bounds for the complexity of continuation methods, On the probability distribution of condition numbers of complete intersection varieties and the average radius of convergence of Newton's method in the underdetermined case

Cites Work

• Complexity of Bezout's theorem. III: Condition number and packing
• On a theory of computation and complexity over the real numbers: 𝑁𝑃- completeness, recursive functions and universal machines
• Complexity of Bezout’s Theorem IV: Probability of Success; Extensions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item