An adaptive Newton algorithm based on numerical inversion: Regularization as postconditioner

DOI10.1007/BF01389880zbMath0579.65046OpenAlexW2033669963MaRDI QIDQ1067360

Joseph W. Jerome

Publication date: 1985

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133027

zbMATH Keywords

finite element methodregularizationnumerical inversionNewton methodsNash-Moser iterationsmoothing operatorsinverse approximationsloss of derivative

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Newton's method for gradient equations based upon the fixed point map: Convergence and complexity study, On a general iterative scheme for newton-type methods, A Nash-Hörmander iteration and boundary elements for the Molodensky problem, Numerical approximation of PDE system fixed-point maps via Newton's method, Algorithms defined by Nash iteration: Some implementations via multilevel collocation and smoothing, Newton iteration with multiquadrics for the solution of nonlinear PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximate Newton methods and homotopy for stationary operator equations
• Global approximate Newton methods
• The boundary problems of physical geodesy
• Approximation of nonlinear evolution systems
• On the Quasi-Optimality in $L_\infty$ of the $\overset{\circ}{H}^1$-Projection into Finite Element Spaces*
• Optimal L ∞ Error Estimates for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems
• Metric entropy and approximation
• On Finite Element Matrices