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

DOI10.1007/s10492-005-0017-zzbMath1099.65033OpenAlexW2050338537MaRDI QIDQ851678

János Karátson

Publication date: 21 November 2006

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

Full work available at URL: https://eudml.org/doc/33221

zbMATH Keywords

conjugate gradient methodmesh independencepreconditioning operator

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

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Cites Work

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• Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators
• On the theory of equivalent operators and application to the numerical solution of uniformly elliptic partial differential equations
• Superlinear Convergence of Conjugate Gradients
• Some Convergence Properties of the Conjugate Gradient Method in Hilbert Space
• ON THE RATE OF CONVERGENCE OF THE CONJUGATE GRADIENT METHOD FOR LINEAR OPERATORS IN HILBERT SPACE
• Preconditioning by Fast Direct Methods for Nonself-Adjoint Nonseparable Elliptic Equations
• Some Superlinear Convergence Results for the Conjugate Gradient Method
• The Methods of Cyclic Reduction, Fourier Analysis and the FACR Algorithm for the Discrete Solution of Poisson’s Equation on a Rectangle
• Marching Algorithms for Elliptic Boundary Value Problems. I: The Constant Coefficient Case
• Marching Algorithms for Elliptic Boundary Value Problems. II: The Variable Coefficient Case
• Optimal Equivalent Preconditioners
• A Parallel Fast Direct Solver for Block Tridiagonal Systems with Separable Matrices of Arbitrary Dimension
• Variable Preconditioning via Quasi-Newton Methods for Nonlinear Problems in Hilbert Space
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• On the regularity of the solution of the Poisson problem on a domain with boundary locally similar to the boundary of a convex open set
• Methods of conjugate gradients for solving linear systems
• On the sublinear and superlinear rate of convergence of conjugate gradient methods