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Picard iteration methods for a spherical atmosphere
Journal of Quantitative Spectroscopy and Radiative Transfer, 2009Several methods for solving the radiative transfer equation in a spherical atmosphere are presented. These methods include the long characteristic Picard iteration, and the conventional and the accelerated short characteristic Picard iteration. Approximate methods as for instance the Picard iteration methods with open boundaries are also discussed. The
Doicu, Adrian, Trautmann, Thomas
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The Picard–HSS iteration method for absolute value equations
Optimization Letters, 2014\textit{O. L. Mangasarian} [ibid. 3, No. 1, 101--108 (2009; Zbl 1154.90599)] proposed a generalized Newton method for the absolute value equation (AVE) \(Ax - |x| = b\) and investigated its convergence properties. This paper deals with the convergence of the Picard-HSS iteration method to solve AVE, where \(A\) is a non-symmetric positive definite ...
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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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Picard iterations of boundary-layer equations
7th Computational Fluid Dynamics Conference, 1985A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions.
M. ARDEMA, L. YANG
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Chebyshev acceleration of picard-lindelöf iteration
BIT, 1992This paper complements recent work by \textit{R.D. Skeel} [SIAM J. Sci. Stat. Comput. 10, No. 4, 756-776 (1989; Zbl 0687.65076) and \textit{O. Nevanlinna} [Numer. Math. 57, No. 2, 147-156 (1990; Zbl 0697.65058)] regarding the question as to whether a significant acceleration of waveform iteration (Picard-Lindelöf iteration) is possible.
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Picard Iteration, Chebyshev Polynomials and Chebyshev-Picard Methods: Application in Astrodynamics
The Journal of the Astronautical Sciences, 2013This paper extends previous work on parallel-structured Modified Chebyshev Picard Iteration (MCPI) Methods. The MCPI approach iteratively refines path approximation of the state trajectory for smooth nonlinear dynamical systems and this paper shows that the approach is especially suitable for initial value problems of astrodynamics.
John L. Junkins +3 more
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Picard iterative approach for \(\psi\)-Hilfer fractional differential problem
2023Summary: In present work, we discuss local existance and uniqueness of solution to the \(\psi\)-Hilfer fractional differential problem. By using the Picard successive approximations, we construct a computable iterative scheme uniformly approximating solution. Two illustrative examples are given to support our findings.
Pawar, Eknath D., Dhaigude, Ramkrishna
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