Fixed-point iteration ≈ Fixed-point iteration
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Stochastic Quasi-Fejér Block-Coordinate Fixed Point Iterations with Random Sweeping Open
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Numerical reckoning fixed points for Suzuki’s generalized nonexpansive mappings via new iteration process Open
In this paper we propose a new three-step iteration process, called M iteration process, for approximation of fixed points. Some weak and strong convergence theorems are proved for Suzuki generalized nonexpansive mappings in the setting of…
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A new iteration scheme for approximating fixed points of nonexpansive mappings Open
In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is…
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Anderson accelerated fixed-stress splitting schemes for consolidation of unsaturated porous media Open
In this paper, we study the robust linearization of nonlinear poromechanics of unsaturated materials. The model of interest couples the Richards equation with linear elasticity equations, employing the equivalent pore pressure. In practice…
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An Efficient Policy Iteration Algorithm for Dynamic Programming Equations Open
We present an accelerated algorithm for the solution of static Hamilton–Jacobi–Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear convergen…
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Asymptotic solutions in asymptotic safety Open
We explain how to find the asymptotic form of fixed point solutions in\nfunctional truncations, in particular $f(R)$ approximations. We find that\nquantum fluctuations do not decouple at large $R$, typically leading to\nelaborate asymptoti…
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On the convergence rate of the Halpern-iteration Open
In this work, we give a tight estimate of the rate of convergence for the Halpern-iteration for approximating a fixed point of a nonexpansive mapping in a Hilbert space. Specifically, using semidefinite programming and duality we prove tha…
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Efficient and practical Newton solvers for non-linear Stokes systems in geodynamic problems Open
Many problems in geodynamic modelling result in a non-linear Stokes problem in which the viscosity depends on the strain rate and pressure (in addition to other variables). After discretization, the resulting non-linear system is most comm…
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A solution of delay differential equations via Picard–Krasnoselskii hybrid iterative process Open
The purpose of this paper is to introduce Picard–Krasnoselskii hybrid iterative process which is a hybrid of Picard and Krasnoselskii iterative processes. In case of contractive nonlinear operators, our iterative scheme converges faster th…
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Some fixed point results for a new three steps iteration process in Banach spaces Open
In this paper, we introduce a three step iteration method and show that this method can be used to approximate fixed point of weak contraction mappings.Furthermore, we prove that this iteration method is equivalent to Mann iterative scheme…
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Globally Convergent Type-I Anderson Acceleration for Non-Smooth Fixed-Point Iterations Open
We consider the application of the type-I Anderson acceleration to solving general non-smooth fixed-point problems. By interleaving with safe-guarding steps, and employing a Powell-type regularization and a re-start checking for strong lin…
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On a new iteration scheme for numerical reckoning fixed points of Berinde mappings with convergence analysis Open
The aim of this work is to introduce a new three step iteration scheme for approximating fixed points of the nonlinear self mappings on a normed linear spaces satisfying Berinde contractive condition.We also study the sufficient condition …
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Reconstruction of the temporal component in the source term of a (time-fractional) diffusion equation Open
In this article, we consider the reconstruction of $\\rho(t)$ in the\n(time-fractional) diffusion equation\n$(\\partial_t^\\alpha-\\triangle)u(x,t)=\\rho(t)g(x)$ ($0<\\alpha \\le 1$) by the\nobservation at a single point $x_0$. We are main…
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A Picard-S iterative method for approximating fixed point of weak-contraction mappings Open
We study the convergence analysis of a Picard-S iterative method for a particular class of weakcontraction mappings and give a data dependence result for fixed points of these mappings. Also, we show that the Picard-S iterative method can …
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Rate optimal adaptive FEM with inexact solver for nonlinear operators Open
We prove convergence with optimal algebraic rates for an adaptive finite\nelement method for nonlinear equations with strongly monotone operator. Unlike\nprior works, our analysis also includes the iterative and inexact solution of\nthe ar…
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A fixed-point current injection power flow for electric distribution systems using Laurent series Open
This paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newton-like iterative procedure…
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Accelerated Mann and CQ algorithms for finding a fixed point of a nonexpansive mapping Open
The purpose of this paper is to present accelerations of the Mann and CQ algorithms. We first apply the Picard algorithm to the smooth convex minimization problem and point out that the Picard algorithm is the steepest descent method for s…
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Some Matrix Iterations for Computing Generalized Inverses and Balancing Chemical Equations Open
An application of iterative methods for computing the Moore–Penrose inverse in balancing chemical equations is considered. With the aim to illustrate proposed algorithms, an improved high order hyper-power matrix iterative method for compu…
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Fixed Point Approximation of Suzuki Generalized Nonexpansive Mappings via New Faster Iteration Process Open
In this paper we propose a new iteration process, called the K iteration process, for approximation of fixed points. We show that our iteration process is faster than the existing leading iteration processes like Picard-S iteration process…
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Numerical approximation of BSDEs using local polynomial drivers and branching processes Open
We propose a new numerical scheme for Backward Stochastic Differential Equations (BSDEs) based on branching processes. We approximate an arbitrary (Lipschitz) driver by local polynomials and then use a Picard iteration scheme. Each step of…
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On Some Iterative Numerical Methods for Mixed Volterra–Fredholm Integral Equations Open
In this paper, we propose a class of simple numerical methods for approximating solutions of one-dimensional mixed Volterra–Fredholm integral equations of the second kind. These methods are based on fixed point results for the existence an…
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Convergence of the EDIIS Algorithm for Nonlinear Equations Open
The Energy Direct Inversion on the Iterative Subspace (EDIIS) algorithm was designed to globalize Anderson acceleration, a method for improving the performance of fixed point iteration. The motivating application is electronic structure co…
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Improving the convergence behaviour of a fixed‐point‐iteration solver for multiphase flow in porous media Open
Summary A new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented. The governing equations are discretized in time using an adaptive θ ‐method. However, the use of implicit discretizations does…
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Remarks on the terminology of the mappings in fixed point iterative methods in metric spaces Open
In this paper we present some suggestions for unifying the terminology of the mappings appearing in fixed point iterative methods for the case when the setting is a metric space.We consider the following concepts: contraction type mapping,…
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On the Iteration Complexity of Hypergradient Computation Open
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include hyperparam…
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Some Step Methods Applied to Nonlinear Equation Open
In the present work, we exhibit a third order family of a new iteration method Dekker's and Classic Chord methods for solving nonlinear equations of single diode solar cell model. These methods have free from computation of second order de…
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Chebyshev Periodical Successive Over-Relaxation for Accelerating Fixed-Point Iterations Open
A novel method which is called the Chebyshev inertial iteration for accelerating the convergence speed of fixed-point iterations is presented. The Chebyshev inertial iteration can be regarded as a valiant of the successive over relaxation …
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Multiple Revolution Solutions for the Perturbed Lambert Problem using the Method of Particular Solutions and Picard Iteration Open
We present a new method for solving the multiple revolution perturbed Lambert problem using the method of particular solutions and modified Chebyshev-Picard iteration. The method of particular solutions differs from the well-known Newton-s…
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A comparison of some fixed point iteration procedures by using the basins of attraction Open
Several iterative processes have been defined by researchers to approximate the fixed points of various classes operators. In this paper we present, by using the basins of attraction for the roots of some complex polynomials, an empirical …
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Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods Open
The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equ…