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Current issues in the development of the theory of iterative methods with Chebyshev acceleration [PDF]

Cybernetics and Systems Analysis, 1993
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Modified Chebyshev-Picard Iteration Methods for Orbit Propagation

The Journal of the Astronautical Sciences, 2011
Modified Chebyshev-Picard Iteration methods are presented for solving high precision, long-term orbit propagation problems. Fusing Chebyshev polynomials with the classical Picard iteration method, the proposed methods iteratively refine an orthogonal function approximation of the entire state trajectory, in contrast to traditional, step-wise, forward ...
Xiaoli Bai, John L. Junkins
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Chebyshev filtering Lanczos' process in the subspace iteration method

International Journal for Numerical Methods in Engineering, 1984
AbstractBathe's basic algorithm of subspace iteration for the solution of the symmetric eigenvalue problem is improved by including a Chebyshev filtering mechanism. To obtain satisfactory convergence for the largest eigenvalues, a shifting strategy is adopted. The shift factor is approximately computed by the Lanczos process.
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A cyclic iterative Chebyshev method for unconstrained minimization of functions

Russian Journal of Numerical Analysis and Mathematical Modelling, 1992
Summary: A cyclic iterative Chebyshev method with the stable realization of each calculation cycle is proposed. The method is used for the unconstrained minimization of twice continuously differentiable strongly convex functions. The convergence rate of the method is studied.
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CONSTRUCTION OF DERIVATIVE-FREE ITERATIVE METHODS FROM CHEBYSHEV'S METHOD

Analysis and Applications, 2013
From some modifications of Chebyshev's method, we consider a uniparametric family of iterative methods that are more efficient than Newton's method, and we then construct two iterative methods in a similar way to the Secant method from Newton's method. These iterative methods do not use derivatives in their algorithms and one of them is more efficient ...
M. A. Hernández, José Antonio Ezquerro, Miquel Grau-Sánchez, Angela Grau   +3 more
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Iterative Chebyshev approximation method for optimal control problems

ISA Transactions
We present a novel numerical approach for solving nonlinear constrained optimal control problems (NCOCPs). Instead of directly solving the NCOCPs, we start by linearizing the constraints and dynamic system, which results in a sequence of sub-problems. For each sub-problem, we use finite number of Chebyshev polynomials to estimate the control and state ...
Di Wu, Changjun Yu, Hailing Wang, Yanqin Bai, Kok-Lay Teo, Kim-Chuan Toh   +5 more
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An iterative method with Chebyshev parameters for finding the maximum eigenvalue and corresponding eigenfunction

USSR Computational Mathematics and Mathematical Physics, 1977
Abstract To accelerate the convergence of the iterations when finding the maximum eigenvalue and corresponding eigenfunction, a method is proposed which employs infinite sequences of Chebyshev parameters and guarantees stability of the computations. A generalization of Bernoulli's method is constructed.
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Utilization of ordered chebyshev parameters in iterative methods

USSR Computational Mathematics and Mathematical Physics, 1976
S.A. Finogenov, V.I. Lebedev
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Bearing fault diagnosis based on EMD and improved Chebyshev distance in SDP image

Measurement: Journal of the International Measurement Confederation, 2021
Yongjian Sun
exaly  

Solution of the parameter ordering problem in Chebyshev iterative methods

USSR Computational Mathematics and Mathematical Physics, 1974
S.A. Finogenov, V.I. Lebedev
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