On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems

DOI10.1016/0024-3795(83)80026-3zbMath0535.65018OpenAlexW1995020472MaRDI QIDQ791277

Kang C. Jea, David M. Young

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1016/0024-3795(83)80026-3

zbMATH Keywords

Lanczos methodconjugate-gradient methodsnonsymmetrizable linear systems

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items

Variations of the GMRES iterative method, Treatment of near-breakdown in the CGS algorithm, On the convergence of Q-OR and Q-MR Krylov methods for solving nonsymmetric linear systems, Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms, Look-ahead in Bi-CGSTAB and other product methods for linear systems, Breakdowns and stagnation in iterative methods, Accuracy and convergence of element‐by‐element iterative solvers for incompressible fluid flows using penalty finite element model, Multigrid methods to accelerate convergence of element-by-element solution algorithms for viscous incompressible flows, Implicit finite element methods for two-phase flow in oil reservoirs, Properties of generalized conjugate gradient methods, Two-dimensional finite element model of breast cancer cell motion through a microfluidic channel, Numerical simulation of forming processes using a coupled fluid flow and heat transfer model, The use of conjugate gradients methods with a segregated finite volume procedure for solving transient, incompressible Navier–Stokes equations, The concept of special inner products for deriving new conjugate gradient‐like solvers for non‐symmetric sparse linear systems, On the roots of the orthogonal polynomials and residual polynomials associated with a conjugate gradient method, GMRES algorithms over 35 years, Iterative algorithms and software for solving large sparse linear systems, Mathematical modelling of chemical engineering systems by finite element analysis using PDE/PROTRAN, Preconditioned biconjugate gradient methods for numerical reservoir simulation, A numerical comparison of conjugate gradient-like methods, Penalty finite element analysis of incompressible flows using element by element solution algorithms, An introduction to the NSPCG software package, Iterative methods for stabilized mixed velocity-pressure finite elements, Recursive interpolation algorithm: A formalism for solving systems of linear equations. II: Iterative methods, Lanczos-type algorithms for solving systems of linear equations, Recent computational developments in Krylov subspace methods for linear systems, Laminar pulsatile two-phase non-Newtonian flow through a pipe, On vector Hankel determinants, The matrix and polynomial approaches to Lanczos-type algorithms, Modified Lanczos method for solving large sparse linear systems

Cites Work

• Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations
• Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• Numerical solution of nonlinear elliptic partial differential equations by a generalized conjugate gradient method
• Iterative methods for solving linear equations
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
• Solution of Sparse Indefinite Systems of Linear Equations
• Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
• A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
• The Lanczos Algorithm with Selective Orthogonalization
• The method of minimum iterations with minimum errors for a system of linear algebraic equations with a symmetrical matrix
• The Conjugate Gradient Method for Linear and Nonlinear Operator Equations
• Hyperbolic Pairs in the Method of Conjugate Gradients
• The Conjugate Residual Method for Constrained Minimization Problems
• The Use of Pre-conditioning in Iterative Methods for Solving Linear Equations with Symmetric Positive Definite Matrices
• The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Methods of conjugate gradients for solving linear systems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item