On generalizations of the theory of consistent orderings for successive overrelaxation methods

DOI10.1007/BF02162914zbMath0172.18802MaRDI QIDQ2532073

Yanyan Li

Publication date: 1968

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131866

zbMATH Keywords

numerical analysis

Related Items (21)

A historical overview of iterative methods ⋮ Generalized consistent orderings and the accelerated overrelaxation method ⋮ On a matrix identity connecting iteration operators associated with a \(p\)-cyclic matrix ⋮ Stepsize restrictions for stability in the numerical solution of ordinary and partial differential equations ⋮ A survey of the iterative methods for the solution of linear systems by extrapolation, relaxation and other techniques ⋮ Exact SOR convergence regions for a general class of \(p\)-cyclic matrices ⋮ On exact convergence of the accelerated overrelaxation method when applied to consistently ordered systems ⋮ The relationship between the Jacobi and the successive overrelaxation (SOR) matrices of a k-cyclic matrix ⋮ On the convergence domains of the \(p\)-cyclic SOR ⋮ Computational methods of linear algebra ⋮ The Kahan S.O.R. convergence bound for nonsingular and irreducible M- matrices ⋮ Domains of divergence of the USSOR method applied on p-cyclic matrices ⋮ On the optimum relaxation factor associated with \(p\)-cyclic matrices ⋮ The extrapolated gauss-seidel plus semi-iterative method for generalized consistently ordered matrices ⋮ The extrapolated gauss-seidel methods and generally consistently ordered matrices ⋮ On the convergence of the modified accelerated overrelaxation (MAOR) method ⋮ Controlled overrelaxation method and the general extrapolation method ⋮ Generalised consistent ordering and the optimum successive overrelaxation factor ⋮ A generalisation of systematic relaxation methods for consistently ordered matrices ⋮ Successive overrelaxation (SOR) and related methods ⋮ Some recent results on the modified SOR theory

Cites Work

• Unnamed Item
• On the successive over-relaxation method for cyclic operators
• Chebyshev semi-iterative methods, successive overrelaxation iterative methods, and second order Richardson iterative methods. I, II
• On infinitesimal conformal and projective transformations of normal contact spaces
• Block iterative methods for cyclically reduced matrix equations
• Positive operators and an inertia theorem
• Some generalisations of the theory of successive over-relaxation
• An application of p-cyclic matrices, for solving periodic parabolic problems
• The index of primitivity of a non-negative matrix
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Estimation of the Relaxation Factor for Small Mesh Size
• A Method of Block Iteration
• A Comparison of the Successive Overrelaxation Method and Semi-Iterative Methods Using Chebyshev Polynomials
• A Method of Normalized Block Iteration
• The Determination of the Optimum Accelerating Factor for Successive Over-relaxation
• Note on the Line Over-relaxation Factor for Small Mesh Size
• Scaled Iterations and Linear Equations
• Symmetric Successive Overrelaxation In Solving Diffusion Difference Equations
• Iterative Methods for Linear Equations with Symmetric Positive Definite Matrix
• The Generalized Overrelaxation Method for the Approximate Solution of Operator Equations in Hilbert Space
• Simultaneous, Successive and Alternating Direction Iteration Schemes
• On complex successive overrelaxation
• An Iterative Process for Optimizing Symmetric Successive Over-Relaxation
• Eigenvectors of the Successive Over-Relaxation Process, and its Combination with Chebyshev Semi-Iteration
• Estimation of the Successive Over-Relaxation Factor
• The Block Symmetric Successive Overrelaxation Method
• On the equivalence of SOR, SSOR and USSOR as applied to  1-ordered systems of linear equations
• The extrapolated modified Aitken iteration method applied to  1-ordered systems of linear equations
• A Method for Finding the Optimum Successive Over-Relaxation Parameter
• The Partitioning of Network Equations for Block Iteration
• Ordering Properties of Linear Successive Iteration Schemes Applied to Multi-Diagonal Type Linear Systems
• On the Round-Off Error in the Method of Successive Over-Relaxation
• On Convergence Criteria for the Method of Successive Over-Relaxation
• The Extrapolated Modified Aitken Iteration Method for Solving Elliptic Difference Equations
• Iterative Methods for Solving Partial Difference Equations of Elliptic Type
• On the Numerical Solution of Elliptic Difference Equations

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