Iterative k-step methods for computing possibly repulsive fixed points in Banach spaces

DOI10.1016/0022-247X(87)90167-3zbMath0635.65070OpenAlexW2058413386MaRDI QIDQ1097647

André Kaiser, Martin H. Gutknecht

Publication date: 1987

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(87)90167-3

zbMATH Keywords

fixed pointBanach spacelocal convergenceasymptotically stationary iterative k-step methodsJacobi-Picard iteration

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

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

Cites Work

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• Über die Methode sukzessiver Approximationen
• A study of semiiterative methods for nonsymmetric systems of linear equations
• k-step iterative methods for solving nonlinear systems of equations
• On a class of Chebyshev approximation problems which arise in connection with a conjugate gradient type method
• On the application of orthogonal polynomials to the iterative solution of linear systems of equations with indefinite or non-Hermitian matrices
• 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
• Asymptotic behavior of nonexpansive mappings
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
• Fixed point theory for nonexpansive mappings. II
• Accelerating the Jacobi Method for Solving Simultaneous Equations by Chebyshev Extrapolation When the Eigenvalues of the Iteration Matrix are Complex
• Concerning the convergence of iterates to fixed points
• Über Toeplitzsche Iterationsverfahren und einige ihrer Anwendungen in der konstruktiven Fixpunkttheorie
• Averaging iteration in a Banach space
• On the Mann Iterative Process
• Rates of Convergence for a Class of Iterative Procedures
• Mean Value Methods in Iteration