A link between the steepest descent method and fixed-point iterations (Q2678996)

scientific article; zbMATH DE number 7643569

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English	A link between the steepest descent method and fixed-point iterations	scientific article; zbMATH DE number 7643569

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instance of

scholarly article

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title

A link between the steepest descent method and fixed-point iterations (English)

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18 January 2023

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full work available at URL

https://arxiv.org/abs/2109.09108

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zbMATH Keywords

fixed-point iterations

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steepest descent method

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preconditioned conjugate gradient method

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preconditioning operator

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Sobolev gradient

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describes a project that uses

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On nonlinear generalized conjugate gradient methods

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Double Sobolev gradient preconditioning for nonlinear elliptic problems

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Equivalent operator preconditioning for elliptic problems

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Variable preconditioning for strongly nonlinear elliptic problems

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Quasi-Newton variable preconditioning for nonlinear nonuniformly monotone elliptic problems posed in Banach spaces

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Novel preconditioners based on quasi-Newton updates for nonlinear conjugate gradient methods

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On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations

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Q4788109

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Function minimization by conjugate gradients

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Rate optimality of adaptive finite element methods with respect to overall computational costs

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Rate optimal adaptive FEM with inexact solver for nonlinear operators

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Convergence of an adaptive Kačanov FEM for quasi-linear problems

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Convergence and quasi-optimal cost of adaptive algorithms for nonlinear operators including iterative linearization and algebraic solver

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Q5479892

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Energy contraction and optimal convergence of adaptive iterative linearized finite element methods

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An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids

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Adaptive iterative linearization Galerkin methods for nonlinear problems

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On the convergence of adaptive iterative linearized Galerkin methods

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Sobolev Gradient Flow for the Gross--Pitaevskii Eigenvalue Problem: Global Convergence and Computational Efficiency

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Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators.

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Sobolev gradient preconditioning for elliptic reaction-diffusion problems with some nonsmooth nonlinearities

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Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space

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Preconditioning operators and Sobolev gradients for nonlinear elliptic problems

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Sobolev gradient preconditioning for the electrostatic potential equation

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Q4237537

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A convergence result for discrete steepest descent in weighted Sobolev spaces

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Q4208365

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Solving boundary value problems numerically using steepest descent in Sobolev spaces

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Q4701933

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Application of Sobolev gradient method to Poisson-Boltzmann system

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Approximate solutions to Poisson-Boltzmann systems with Sobolev gradients

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Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs

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Optimal Equivalent Preconditioners

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Preconditioning and Boundary Conditions

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Q3785223

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Q3317432

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Q3673554

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Sobolev gradients and differential equations

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Minimal Surfaces and Sobolev Gradients

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Q4379826

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Q5563083

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The conjugate gradient method in extremal problems

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Q3313210

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Conjugate gradient algorithms in nonconvex optimization

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Polynomial solution of singular differential equations using Weighted Sobolev gradients

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Numerical approximation of time evolution related to Ginzburg-Landau functionals using weighted Sobolev gradients

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Numerical solution of Burgers equation by the Sobolev gradient method

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NUMERICAL SOLUTIONS OF INTEGRO-DIFFERENTIAL EQUATIONS USING SOBOLEV GRADIENT METHODS

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Sobolev gradient approach for the time evolution related to energy minimization of Ginzburg-Landau functionals

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Approximating time evolution related to Ginzburg-Landau functionals via Sobolev gradient methods in a finite-element setting

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Energy minimization using Sobolev gradients: application to phase separation and ordering.

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Convergence Conditions for Ascent Methods

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Convergence Conditions for Ascent Methods. II: Some Corrections

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Identifiers

Mathematics Subject Classification ID

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10.1007/S11590-022-01867-9

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Mathematics(1 entry)

mardi Publication:2678996