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Estimate for Picard iterations of a Hermitian matrix operator
The purpose of this paper is to study the Picard iterations of a Hermitian matrix operator. In [1], we proved the existence and uniqueness of attractive fixed point of an operator defined on Hermitian matrix space and satisfying a certain condition. In this paper we show that the n th Picard iterations of that Hermitian matrix operator converges to the
Habibulla Akhadkulov
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Parallel Numerical Picard Iteration Methods
Journal of Scientific Computing, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Picard iteration and its application
Linear and Multilinear Algebra, 2006The convergence behavior of the Picard iteration Xk+1=AXk+B and the weighted case Yk=Xk/bk is investigated. It is shown that the convergence of both these iterations is related to the so-called effective spectrum of A with respect to some matrix. As an application of our convergence results we discuss the convergence behavior of a sequence of scaled ...
Xuzhou Chen, Robert E Hartwig
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Adaptive Underrelaxation of Picard Iterations in Ground Water Models
Ground Water, 2007Abstract This methods note examines the use of adaptive underrelaxation of Picard iterations to accelerate the solution convergence for nonlinear ground water flow problems. Ground water problems are nonlinear when drains, phreatophytes, stream aquifer, and similar features are simulated.
Timothy, Durbin, David, Delemos
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