Can Adaption Help on the Average.
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Caractérisations de la convergence locale de la méthode des approximations successives
Michel Cosnard (1977)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Cases when the use of the analytic method for solving differential equations is better than the use of numerical ones
K. Orlov (1980)
Matematički Vesnik
Common fixed points of a finite family of asymptotically pseudocontractive maps.
Osilike, M.O., Akuchu, B.G. (2004)
Fixed Point Theory and Applications [electronic only]
Common solutions of an iterative scheme for variational inclusions, equilibrium problems, and fixed point problems.
Peng, Jian-Wen, Wang, Yan, Shyu, David S., Yao, Jen-Chih (2008)
Journal of Inequalities and Applications [electronic only]
Comparing the radii of some balls appearing in connection to three local convergence theorems for Newton's method.
Argyros, Ioannis K. (1998)
Southwest Journal of Pure and Applied Mathematics [electronic only]
Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces.
Babu, G.V.R., Prasad, K.N.V.V.Vara (2006)
Fixed Point Theory and Applications [electronic only]
Comparison theorems for weak splittings of bounded operators.
Ivo Marek, Daniel B. Szyld (1990/1991)
Numerische Mathematik
Computation of derivatives in the finite element method
Ivo Babuška (1970)
Commentationes Mathematicae Universitatis Carolinae
Computer-assisted proofs for fixed point problems in Sobolev spaces.
Schenkel, Alain, Wehr, Jan, Wittwer, Peter (2000)
Mathematical Physics Electronic Journal [electronic only]
Computing the numerical range of Krein space operators
Natalia Bebiano, J. da Providência, A. Nata, J.P. da Providência (2015)
Open Mathematics
Consider the Hilbert space (H,〈• , •〉) equipped with the indefinite inner product[u,v]=v*J u,u,v∈ H, where J is an indefinite self-adjoint involution acting on H. The Krein space numerical range WJ(T) of an operator T acting on H is the set of all the values attained by the quadratic form [Tu,u], with u ∈H satisfying [u,u]=± 1. We develop, implement and test an alternative algorithm to compute WJ(T) in the finite dimensional case, constructing 2 by 2 matrix compressions of T and their easily determined...
Concerning the convergence of a modified Newton-like method.
Argyros, Ioannis K. (1999)
Zeitschrift für Analysis und ihre Anwendungen
Concerning the rate of convergence of Newton's process
Vlastimil Pták (1975)
Commentationes Mathematicae Universitatis Carolinae
Conditions de convergence pour les algorithmes itératifs monotones, autonomes et non déterministes
Gérard G. L. Meyer (1977)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Cones and error bounds for linear iterations.
George J. Miel (1980)
Aequationes mathematicae
Contractivity in the Numerical Solution of Initial Value Problems.
M.N. Spijker (1983)
Numerische Mathematik
Convergence analysis of a one-step intermediate Newton iterative scheme.
Uko, Livinus U., Velásquez Ossa, Raúl Eduardo (2001)
Revista Colombiana de Matemáticas
Convergence analysis of finite difference schemes for semi-linear initial-value problems
J. Löfström, V. Thomée (1976)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
Convergence comparison of several iteration algorithms for the common fixed point problems.
Song, Yisheng, Liu, Xiao (2009)
Fixed Point Theory and Applications [electronic only]
Convergence conditions for Secant-type methods
Ioannis K. Argyros, Said Hilout (2010)
Czechoslovak Mathematical Journal
We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier conditions...
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