Convergence of the Arnoldi process when applied to the Picard-Lindelöf iteration operator
BIT, 1996 In this paper the iteration operator corresponding to the Picard-Lindelöf iteration is considered as a model case in order to investigate the convergence theory of the Arnoldi process.
Hyvönen, Saara, Hyvönen, S.
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A study of Mandelbrot and Julia Sets via Picard-Thakur iteration with s-convexity. [PDF]
PLoS OneNowadays, many researchers are employing various iterative techniques to analyse the dynamics of fractal patterns. In this paper, we explore the formation of Mandelbrot and Julia sets using the Picard-Thakur iteration process, extended with s-convexity ...
Nawaz B, Gdawiec K, Ullah K, Aphane M.
europepmc +2 more sources
Convergence analysis of Suzuki's generalized nonexpansive mappings using the Picard-Abbas iteration process. [PDF]
PLoS ONEThis manuscript investigates the convergence behavior of Suzuki's generalized nonexpansive mappings using the recently introduced Picard-Abbas iteration process.
Bashir Nawaz +4 more
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Assessing the benefits of approximately exact step sizes for Picard and Newton solver in simulating ice flow (FEniCS-full-Stokes v.1.3.2) [PDF]
Geoscientific Model DevelopmentSolving the momentum balance is the computationally expensive part of simulating the evolution of ice sheets. The momentum balance is described by the nonlinear full-Stokes equations, which are solved iteratively. We use the Picard iteration and Newton's
N. Schmidt +4 more
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Mathematics, 2020 In this paper, we prove two general convergence theorems with error estimates that give sufficient conditions to guarantee the local convergence of the Picard iteration in arbitrary normed fields. Thus, we provide a unified approach for investigating the
Stoil I. Ivanov
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Generation of Antifractals via Hybrid Picard-Mann Iteration [PDF]
IEEE Access, 2020 The aim of this paper is to generate antifractals using fixed point iterative algorithms, i.e., we aim to generate anti Julia sets, tricorns and multicorns for the anti-polynomial z → z̅k +c of the complex polynomial zk +c, for k ≥ 2.
Wei Wang +3 more
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Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration [PDF]
Fixed Point Theory and Applications, 2010 This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and ...
De la Sen M
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Introduction of new Picard–S hybrid iteration with application and some results for nonexpansive mappings [PDF]
Arab Journal of Mathematical Sciences, 2022 Purpose – In this paper, Picard–S hybrid iterative process is defined, which is a hybrid of Picard and S-iterative process. This new iteration converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, S-iteration, Picard–Mann hybrid, Picard ...
Julee Srivastava
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A PICARD THEOREM FOR ITERATIVE DIFFERENTIAL EQUATIONS [PDF]
Demonstratio Mathematica, 2009 AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the ...
Li, Wenrong, Cheng, Sui Sun
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Approximation of Fixed Points for Mean Nonexpansive Mappings in Banach Spaces
Journal of Function Spaces, 2021 In this paper, we establish weak and strong convergence theorems for mean nonexpansive maps in Banach spaces under the Picard–Mann hybrid iteration process.
Junaid Ahmad +3 more
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