Stationary and almost stationary iterative (k,l)-step methods for linear and nonlinear systems of equations

DOI10.1007/BF01409784zbMath0685.65044MaRDI QIDQ1262086

Martin H. Gutknecht

Publication date: 1989

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

Full work available at URL: https://eudml.org/doc/133391

zbMATH Keywords

equivalenceconvergencefixed point equationFaber polynomialsmethodChebyshev iterationEulerCharacterizationsalmost stationary iterative methodsstationary semiiterative method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Iterative numerical methods for linear systems (65F10)

Related Items (10)

A mixed finite element for the Stokes problem using quadrilateral elements ⋮ Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain ⋮ A theoretical overview of Krylov subspace methods ⋮ An adaptive method for solving nonsymmetric linear systems involving applications of SCPACK ⋮ A condition for the superiority of the (2, 2)-step methods over the related Chebyshev method ⋮ Unnamed Item ⋮ Is a Chebyshev method optimal for an elliptic region also optimal for a nearly elliptic region? ⋮ Biorthogonal rational Krylov subspace methods ⋮ Implementation of an adaptive algorithm for Richardson's method ⋮ Revisiting \((k,\ell)\)-step methods

Cites Work

• A study of semiiterative methods for nonsymmetric systems of linear equations
• Numerical conformal mapping methods based on function conjugation
• k-step iterative methods for solving nonlinear systems of equations
• Iterative k-step methods for computing possibly repulsive fixed points in Banach spaces
• Rational Chebyshev approximation on the unit disk
• The analysis of k-step iterative methods for linear systems from summability theory
• Iterative solution of linear operator equations in Hilbert space and optimal Euler methods
• On the construction of iteration methods for linear equations in Banach spaces by summation methods
• Iterationsverfahren und allgemeine Euler-Verfahren. (Iterative and general Euler methods)
• Über mehrstufige Iterationsverfahren und die Lösung der Hammersteinschen Gleichung
• Über ein mehrstufiges Iterationsverfahren zur Lösung von linearen Gleichungen
• On the Construction of Semi-Iterative Methods
• General k-Part Stationary Iterative Solutions to Linear Systems
• On Hybrid Semi-Iterative Methods
• Concerning the convergence of iterates to fixed points
• Mean Value Methods in Iteration
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