An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix

Keywords

Mathematics, Conjugate gradient method, Coefficient matrix, Iterative method, Matrix (chemical analysis)

References

• Handbook for Automatic ComputationHeinz Rutishauser — 1960
• The Use of Conjugate Gradients for Systems of Linear Equations Possessing “Property A”John Reid — 1972
• Direct methods in reservoir simulationH.S. Price, K.H. Coats — 1974
• ITERATIVE SOLUTION OF IMPLICIT APPROXIMATIONS OF MULTIDIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONSHerbert L. Stone — 1968
• Note on MatricesJames P. Brill — 1895
• Matrix Iterative AnalysisRichard S. Varga, J. Gillis — 1961
• The Conjugate Gradient Method for Linear and Nonlinear Operator EquationsJames W. Daniel — 1967
• NOTE ON M -MATRICESKy Fan — 1960
• Linear algebraGeetha S. Rao — 1971
• The algebraic eigenvalue problemE. I., J. H. Wilkinson — 1966
• Matrix Iterative AnalysisRichard S. Varga — 2000
• Linear AlgebraKenneth A. Hoffman — 1961
• The algebraic eigenvalue problemJ. H. Wilkinson — 1965

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• Avant-Garde Matrix Splitting for the Solution of Sparse Non-symmetric Linear SystemsAbdullah Shah — 2007
• A numerical solution for the diffusion equation in hydrogeologic systemsAudrey L. Ishii, Richard W. Healy, Robert G. Striegl — 1989
• Preconditioned techniques for large eigenvalue problemsKesheng Wu — 1997
• Semi-Toeplitz preconditioning for linearized boundary layer problemsSamuel Sundberg — 2002
• High-efficiency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equationsGen Li, Chun’an Tang, Lianchong Li — 2013
• Параллельные варианты метода неполного треугольного разложения второго порядка сопряженных градиентов на основе использования специального переупорядочения матрицы коэффициентовО Ю Милюкова — 2014
• Experiments with sparse preconditioning of dense problems from electromagnetic applicationsBruno Carpentieri, I.S. Duff, Luc Giraud — 2013
• Adaptation of the C.H.A.D. computer library to nuclear simulationsDaniel Thomas Rock — 2009
• A comparison of iterative methods for a model coupled system of elliptic equationsJ.M. Donato — 1993
• A VARIABLE PRECONDITIONING USING THE SOR METHOD FOR GCR-LIKE METHODSKuniyoshi Abe, Shao‐Liang Zhang — 2005
• A Semi-Implicit, Three-Dimensional Model for Estuarine CirculationPeter E. Smith — 2006
• Construction and application of hierarchical matrix preconditionersFang Yang — 2008
• Parallel Performance of Block ILU Preconditioners for a Block-tridiagonal MatrixJae Heon Yun — 2004
• An Adaptive CGNR Algorithm for Solving Large Linear SystemsChun-Guang Li — 2001
• Preconditioning sparse matrices for computing eigenvalues and solving linear systems of equationsTzu-Yi Chen, James Demmel — 2001
• Optimal Shape Design Of Aerodynamic Configurations: A Newton-Krylov ApproachMarian Nemec — 2003
• Two classes of preconditioners computed using block matrix factorization techniquesL. S. Baca, Douglas E. Salane — 1987
• Block ILU Preconditioners for a Nonsymmetric Block-Tridiagonal M-MatrixJae Heon Yun — 2000

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