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An Adaptive Chebyshev Iterative Method
Mathematical Models and Computer Simulations, 2018An adaptive Chebyshev iterative method used to solve boundary-value problems for three-dimensional elliptic equations numerically is constructed. In this adaptive method, the unknown lower bound of the spectrum of the discrete operator is refined in the additional iteration cycle, and the upper bound of the spectrum is taken to be its estimate by the ...
V. T. Zhukov +2 more
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Ordering of the iterative parameters in the cyclical Chebyshev iterative method
USSR Computational Mathematics and Mathematical Physics, 1971Abstract A SOLUTION is offered for the problem of ordering the parameters in a cyclical iterative method used for solving the equation Au = f, in such a way as to eliminate computational instability.
S.A. Finogenov, V.I. Lebedev
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Inner and Outer Iterations for the Chebyshev Algorithm
SIAM Journal on Numerical Analysis, 1998The preconditioned Chebyshev iteration is examined in which at each step the linear system involving the preconditioner is solved inexactly by an inner iteration. The tolerance used in the inner iteration is allowed to decrease from one outer iteration to the next. When the tolerance converges to zero, the asymptotic convergence rate is the same as for
Gene H. Golub +2 more
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An Iterative Chebyshev Approximation Method for Network Design [PDF]
IEEE Transactions on Circuit Theory, 1968 One of the most important problems of computeraided network design is the optimization of network characteristics by iterative calculation. In this paper, the problem of realizing a network whose transmission characteristics approximate a given function in Chebyshev sense is treated as a nonlinear programming problem, and a method of solving this ...
Y. Ishizaki, H. Watanabe
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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.
Ahmad Bani Younes +3 more
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Iterative Chebyshev Approximation Technique for Network Synthesis
IEEE Transactions on Circuit Theory, 1967The techniques of mathematical approximation theory are applied to the weighted Chebyshev approximation of general transfer functions, as well as loss and phase characteristics. Various methods are shown for implementing the Remez algorithm for rational approximants, and extensions of the existing approximation theory are provided for functionals of ...
J. Bingham, G.C. Temes
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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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Adaptive Chebyshev Iteration Based on Modified Moments
1993The problem of solving a linear system of equations $$Ax = b\quad A \in {\mathbb{R}^{N \times N}},\quad x,b \in {\mathbb{R}^N}$$ (1) , with a large, sparse and nonsymmetric matrix A arises in many applications. A Chebyshev iterative method based on scaled Chebyshev polynomials p n for an interval in the complex plane can be used to solve (1 ...
Daniela Calvetti +2 more
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Gaussian Quadrature Applied to Adaptive Chebyshev Iteration
1994Chebyshev iteration has been a popular iterative scheme for the solution of large linear systems of equations with a symmetric positive definite matrix A. With the advent of parallel processors, there has been a resurgence of interest in this method. In Chebyshev iteration one determines iteration parameters so that the residual polynomials axe scaled ...
Daniela Calvetti +2 more
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Iterative Chebyshev Polynomial Algorithm for Signal Denoising on Graphs
2019 13th International conference on Sampling Theory and Applications (SampTA), 2019In this paper, we consider the inverse graph filtering process when the original filter is a polynomial of some graph shift on a simple connected graph. The Chebyshev polynomial approximation of high order has been widely used to approximate the inverse filter.
Qiyu Sun +3 more
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