Local convergence analysis of tensor methods for nonlinear equations

DOI10.1007/BF01585177zbMath0796.65069MaRDI QIDQ1321657

Paul D. Frank, Robert B. Schnabel, Dan Feng

Publication date: 13 October 1994

Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)

zbMATH Keywords

local convergencesuperlinear convergencetensor methods

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10)

Related Items

Tensor-Krylov methods for large nonlinear equations ⋮ Practical quasi-Newton algorithms for singular nonlinear systems ⋮ Tensor methods for solving symmetric \({\mathcal {M}}\)-tensor systems ⋮ A modified Brown algorithm for solving singular nonlinear systems with rank defects ⋮ A ABS algorithm for solving singular nonlinear system with space transformation ⋮ Tensor methods for large sparse systems of nonlinear equations ⋮ A globally convergent method for solving nonlinear equations without the differentiability condition

Uses Software

• TENSOLVE
• LINPACK

Cites Work

• Unnamed Item
• Starlike domains of convergence for Newton's method at singularities
• Analysis of Newton’s Method at Irregular Singularities
• A New Acceleration Method for Newton’s Method at Singular Points
• Tensor Methods for Nonlinear Equations
• Convergence Rates for Newton’s Method at Singular Points
• On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions
• Newton’s Method at Singular Points. I
• Newton’s Method at Singular Points. II
• Convergence Acceleration for Newton’s Method at Singular Points
• Tensor Methods for Unconstrained Optimization Using Second Derivatives
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• On Newton’s Method for Singular Problems
• Algorithm 768: TENSOLVE