Results 191 to 200 of about 770,509 (245)
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arXiv.org, 2023
We develop the Akhiezer iteration, a generalization of the classical Chebyshev iteration, for the inner product-free, iterative solution of indefinite linear systems using orthogonal polynomials for measures supported on multiple, disjoint intervals. The
Cade Ballew, T. Trogdon
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We develop the Akhiezer iteration, a generalization of the classical Chebyshev iteration, for the inner product-free, iterative solution of indefinite linear systems using orthogonal polynomials for measures supported on multiple, disjoint intervals. The
Cade Ballew, T. Trogdon
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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
Giladi, Eldar +2 more
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An optimized Chebyshev–Halley type family of multiple solvers: Extensive analysis and applications
Mathematical methods in the applied sciences, 2022In this manuscript, we introduce a higher‐order optimal family of Chebyshev–Halley type methods to solve a univariate nonlinear equation having multiple roots.
L.Vidya rani +3 more
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Accelerating Newton-Schulz Iteration for Orthogonalization via Chebyshev-type Polynomials
arXiv.orgThe problem of computing optimal orthogonal approximation to a given matrix has attracted growing interest in machine learning. Notable applications include the recent Muon optimizer or Riemannian optimization on the Stiefel manifold.
Ekaterina Grishina +2 more
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Chebyshev wavelet-Picard technique for solving fractional nonlinear differential equations
International journal of nonlinear sciences and numerical simulation, 2022In the present paper, an efficient method based on a new kind of Chebyshev wavelet together with Picard technique is developed for solving fractional nonlinear differential equations with initial and boundary conditions.
Xiaoyong Xu, Fengying Zhou
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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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CONSTRUCTION OF DERIVATIVE-FREE ITERATIVE METHODS FROM CHEBYSHEV'S METHOD
Analysis and Applications, 2013From 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 ...
Ezquerro, J. A. +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 ...
G. Temes, J. Bingham
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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.
Lebedev, V. I., Finogenov, S. A.
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Iterative Chebyshev approximation method for optimal control problems
ISA TransactionsWe 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 +5 more
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