ON THE RATE OF CONVERGENCE OF THE CONJUGATE GRADIENT METHOD FOR LINEAR OPERATORS IN HILBERT SPACE

DOI10.1081/NFA-120006694zbMath1011.65026MaRDI QIDQ3148351

Owe Axelsson, János Karátson

Publication date: 14 May 2003

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

zbMATH Keywords

Hilbert spaceunbounded operatorconjugate gradient methodlinear operator equationconjugate gradientbounded operatorelliptic operators.sublinear and superlinear convergence

Mathematics Subject Classification ID

General theory of partial differential operators (47F05) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (12)

Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators. ⋮ Analysis of the Barzilai-Borwein step-sizes for problems in Hilbert spaces ⋮ A monotonicity result for norms in conjugate gradient algorithms ⋮ A posteriori superlinear convergence bounds for block conjugate gradient ⋮ Superlinear PCG Algorithms: Symmetric Part Preconditioning and Boundary Conditions ⋮ Superlinearly convergent CG methods via equivalent preconditioning for nonsymmetric elliptic operators ⋮ Reaching the superlinear convergence phase of the CG method ⋮ Symmetric Part Preconditioning of the CG Method for Stokes Type Saddle-Point Systems ⋮ On the Superlinear Convergence Rate of the Preconditioned CGM for Some Nonsymmetric Elliptic Problems ⋮ Construction of a Preconditioner for General Elliptic Problems Using Riesz Map ⋮ Superlinear Convergence of Krylov Subspace Methods for Self-Adjoint Problems in Hilbert Space ⋮ Analysis of Iterative Methods in Photoacoustic Tomography with Variable Sound Speed

Cites Work

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• Some Superlinear Convergence Results for the Conjugate Gradient Method
• Iterative Solution Methods
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Methods of conjugate gradients for solving linear systems

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