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SPT5 regulates Pol II pausing and elongation in different ways at early versus late embryonic stages
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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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Polynomial acceleration of the Picard-Lindelof iteration
IMA Journal of Numerical Analysis, 1998The effect of polynomial acceleration of the Picard-Lindelöf iteration formula is analyzed for a function \(x(t)\) on a bounded interval. The basic iteration formula for solution to \[ x'(t)+ Ax(t)= f(t),\quad x(0)= x_0,\quad t\in [0,T],\tag{i} \] is \[ x^n= Kx^{n-1}+ g,\quad n=1,2,\dots\quad Kx(t)= \int^t_0 e^{-M(t-s)}Nx(s)ds,\tag{ii} \] \[ g= e^{-Mt ...
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Solving Stiff Problems Using Generalized Picard Iterations
AIP Conference Proceedings, 2009The main point of the talk is an alternative approach to the construction of numerical methods for stiff problems. It can be interpreted as a generalization of fixed‐point iterations for implementation of implicit collocation methods. Proposed algorithms combine easy implementation and low cost of iterations with superior convergence properties on ...
V. V. Bobkov +6 more
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