Picard iteration and convergence
Strong convergence and stability of Picard iteration sequences for a general class of contractive-type mappings
... with Picard iteration was developed for the class of nonexpansive maps because the simpler Picard sequence will not always converge for nonexpansive ...yield convergence of the sequence to a ...
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A convergence theorem of the Picard iteration whose mapping has multiple fixed points
... 2 Major in Interdisciplinary Science and Engineering, Shimane University, Matsue, Shimane, 690-8054, Japan.. Copyright c 2015 Seto and Kuroiwa. This is an open access article distribute[r] ...
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Picard iteration converges faster than Mann iteration for a class of quasi-contractive operators
... In the class of quasi-contractive operators satisfying Zamfirescu’s conditions, the most used fixed point iterative methods, that is, the Picard, Mann, and Ishikawa iterations, are all known to be convergent to ...
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On The Numerical Solution of Picard Iteration Method for Fractional Integro - Differential Equation
... Abstract: In this paper, the concept of Successive Approximation method also called the Picard Iteration Method (PIM) for solving Fractional integro-differential equations is introduced. The fractional ...
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Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind
... numerical Picard iteration methods for nonlinear Volterra integral Equation ...of convergence of the Picard ...the convergence re- ...
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Modified Chebyshev Picard Iteration: Integration of Perturbed Motion using Modified Equinoctial Elements
... the iteration count is initialized and the initial trajectory guess is specified (if no knowledge of the trajectory is applied, this can be a matrix of ones or zeros; instead a “warm start” such as the unperturbed ...
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Enhancements to Chebyshev-Picard Iteration Efficiency for Generally Perturbed Orbits and Constrained Dynamical Systems
... terminal convergence approaches the true system dynamics to within machine ...the convergence process and eliminate slow drift over long time ...intermediate Picard iteration state estimates ...
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On the comparison between Picard Iteration Method and Adomian Decomposition Method in solving non linear differential equations
... accuracy and convergence of the PIM results generally increases when the number of iterations is increased. We can see from table 12 that the error approximation is large for the 2nd and 4th order, but on getting ...
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New Picard S hybrid iteration
... new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard –Mann hybrid, Picard–Krasnoselskii hybrid, Picard–Ishikawa hybrid iterative ...
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Modified Picard-Mann hybrid iteration process for total asymptotically nonexpansive mappings
... new iteration process for nonexpansive mappings, which he called ‘Picard-Mann hybrid iteration process’ and claimed that this process is independent of Picard and Mann iterative process and ...
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Fixed point approximation of Picard normal S-iteration process for generalized nonexpansive mappings in hyperbolic spaces
... The purpose of this paper is to establish strong and D- convergence theorems for a new iteration process gener- ated by generalized nonexpansive mappings in uniformly convex hyperbolic spaces. The theorems ...
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17. Strong convergence of Noor iteration for a general class of functions
... for Picard and Mann iteration processes using the follow- ing contractive condition: there exist b ∈ [0, 1) and a monotone increasing function φ : ℜ + −→ ℜ + with φ(0) = 0 such that for each x, y ∈ ...
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Convergence and summable almost T stability of the random Picard Mann hybrid iterative process
... YM: Convergence and stability of iterative processes for a pair of simultaneously asymptotically quasi-nonexpansive type mappings in convex metric ...Strong convergence theorem and stability problems of ...
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On -Stability of Picard Iteration in Cone Metric Spaces
... Theorem 2.7. Let X, d be a nonempty complete cone metric space, P be a normal cone, and T a quasicontraction and self map of X with some 0 < λ < 1/2. Then Picard’s iteration is T -stable. Proof. By 6, ...
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Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration
... of iteration procedures defined by continuous functions acting on self-maps in continuous metric ...the iteration process can be relaxed to the fulfilment of being large contractions or to be subject to ...
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On the speed of convergence of iteration of a function
... The rates of convergence of the sequence fn(X) have been studied extensively, see Ostrowski [1] or Seneta [3].. If f(0) < 1, the sequence converges at least geometrically fast: There [r] ...
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The convergence of an implicit mean value iteration
... Condition (2.1) forces iteration (1.2) to be well defined. The papers listed above do not impose such a condition, and consequently, the resulting implicit mean value iterations need not be well defined, as the ...
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On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems
... The concept of stability is not very precise because of the sequence {𝑦 𝑛 } 𝑛=0 ∞ which is arbitrary taken. So, it would be more natural that {𝑦 𝑛 } to be an approximate sequence of {𝑥 𝑛 } and Berinde [1] introduced the ...
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Modified Chebyshev-Picard Iteration Methods for Station-Keeping of Translunar Halo Orbits
... Chebyshev-Picard Iteration method is used to compute corrective maneuvers at discrete time intervals for station-keeping of halo orbit satellite, and several key parameters affecting the mission performance ...
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Local convergence of the symmetric rank-one iteration
... Preservation of symmetry is an attractive feature, as is the possibility of storing one vector per iterate in a matrix-free limited memory implementation. However, imple- mentations that store a single vector for each ...
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