Complex conjugate gradient methods

DOI10.1007/BF02145754zbMath0780.65021OpenAlexW2013208486MaRDI QIDQ1801408

Pascal Joly, Gérard A. Meurant

Publication date: 23 January 1994

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02145754

zbMATH Keywords

linear systemsHelmholtz equationcomplex linear systemsconjugate residual methodbiconjugate gradient methodcomplex GMRESbiconjugate gradient squared methodcomplex orthominconjugate gradient-like methodsnon-singular complex matricesnormal equation conjugate gradient method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (11)

Lanczos-type variants of the COCR method for complex nonsymmetric linear systems ⋮ A theoretical overview of Krylov subspace methods ⋮ Unnamed Item ⋮ pyGDM -- a Python toolkit for full-field electro-dynamical simulations and evolutionary optimization of nanostructures ⋮ A new quasi-minimal residual method based on a biconjugate \(A\)-orthonormalization procedure and coupled two-term recurrences ⋮ A fast implementation for GMRES method ⋮ A new iterative method for solving complex symmetric linear systems ⋮ Projection methods for linear systems ⋮ Recursive interpolation algorithm: A formalism for solving systems of linear equations. II: Iterative methods ⋮ Real valued iterative methods for solving complex symmetric linear systems ⋮ Complex solution to nonideal contaminant transport through porous media

Uses Software

• CGS

Cites Work

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• On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• A Taxonomy for Conjugate Gradient Methods
• Incomplete Factorization Methods for Fully Implicit Simulation of Enhanced Oil Recovery
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• How Fast are Nonsymmetric Matrix Iterations?
• Changing the Norm in Conjugate Gradient Type Algorithms
• Variants of BICGSTAB for Matrices with Complex Spectrum
• A Generalization of the Conjugate-Gradient Method to Solve Complex Systems

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