Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms

DOI10.1016/0024-3795(87)90120-0zbMath0632.65030OpenAlexW1989057852MaRDI QIDQ1095577

David M. Young, Wayne D. Joubert

Publication date: 1987

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90120-0

zbMATH Keywords

conjugate gradient methodnon-Hermitian linear systemsORTHODIRORTHOMINORTHORES

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

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A generalized conjugate gradient, least square method ⋮ Parallel multidomain iterative algorithms for the Helmholtz wave equation ⋮ Breakdowns and stagnation in iterative methods ⋮ Investigation of a preconditioner for the \(P_{2} - P_{1}\) finite element solution of Stokes problem ⋮ Artificial damping techniques for scalar waves in the frequency domain ⋮ Block jacobi preconditioning of the conjugate gradient method on a vector processor ⋮ Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory ⋮ On conjugate gradient type methods and polynomial preconditioners for a class of complex non-Hermitian matrices ⋮ On the choice of preconditioner for minimum residual methods for non-Hermitian matrices ⋮ On IOM(q): The Incomplete Orthogonalization Method for Large Unsymmetric Linear Systems ⋮ Recursive interpolation algorithm: A formalism for solving systems of linear equations. II: Iterative methods ⋮ The Arnoldi process, short recursions, and displacement ranks

Cites Work

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• On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
• Approximating the inverse of a matrix for use in iterative algorithms on vector processors
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• The question of non-self-adjoint extension of the conjugate gradients method is closed
• Polynomial Preconditioners for Conjugate Gradient Calculations
• A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
• Orthogonal Error Methods
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• ON DIAGONABLE AND NORMAL MATRICES
• Methods of conjugate gradients for solving linear systems