Portable Fortran subroutines computing the Fermi-Dirac integral F-j(x) and the incomplete Fermi-Dirac integral F-j(x,b) are presented. For the first time a set of series expansions is implemented allowing these specia...
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Portable Fortran subroutines computing the Fermi-Dirac integral F-j(x) and the incomplete Fermi-Dirac integral F-j(x,b) are presented. For the first time a set of series expansions is implemented allowing these special functions to be evaluated efficiently within a prescribed accuracy for real j and x
We propose to map logarithmically converging sequences to linearly converging sequences using interpolation. After this, convergence accelerators for linear convergence become effective. The interpolation approach wor...
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We propose to map logarithmically converging sequences to linearly converging sequences using interpolation. After this, convergence accelerators for linear convergence become effective. The interpolation approach works also if only relatively few members of the problem sequence are known, contrary to several other approaches. The effectiveness of the approach is demonstrated for a particular example. (C) 1998 Elsevier Science Ltd. All rights reserved.
This paper considers the problem of estimating the number of components in a finite mixture of distributions from some parametric families. An estimation procedure using a numerical algorithm for accelerating the conv...
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This paper considers the problem of estimating the number of components in a finite mixture of distributions from some parametric families. An estimation procedure using a numerical algorithm for accelerating the convergence of slowly convergent sequences is developed and its asymptotic properties are investigated. The behavior of the procedure is illustrated with simulated and real data.
Extrapolation methods have been used for many years for numerical integration. The most well-known of these methods is Romberg integration. A survey by Joyce on the use of extrapolation in numerical analysis appeared ...
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It is frustrating when a power (or other) series fails to converge, preventing the straightforward calculation of values of a function of interest. Here, the discussion focuses on two algorithms, discovered long ago b...
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It is frustrating when a power (or other) series fails to converge, preventing the straightforward calculation of values of a function of interest. Here, the discussion focuses on two algorithms, discovered long ago but not well known, by which the sums of series may be calculated arithmetically, notwithstanding the divergence of the series. A powerful example vindicates both methods.
The computation of the responses and their design sensitivities play an essential role in structural analysis and optimization. Significant works have been clone in this area. Modal method is one of the classical meth...
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ISBN:
(纸本)9783037853276
The computation of the responses and their design sensitivities play an essential role in structural analysis and optimization. Significant works have been clone in this area. Modal method is one of the classical methods. In this study, a new error compensation method is constructed, in which the modal superposition method is hybrid with epsilon algorithm for responses and their sensitivities analysis of undamped system. In this study the truncation error of modal superposition is expressed by the first L orders eigenvalues and its eigenvectors explicitly. The epsilon algorithm is used to accelerate the convergence of the tnmcation errors. Numerical examples show that the present method is validity and effectiveness.
In this paper, novel convergence accelerating techniques are adapted onto the proposed hyperbolic numerical inverse Laplace transform method (hyperbolic-NILT) and analyzed. This Ill NILT method is based on the approxi...
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ISBN:
(纸本)9781509040865
In this paper, novel convergence accelerating techniques are adapted onto the proposed hyperbolic numerical inverse Laplace transform method (hyperbolic-NILT) and analyzed. This Ill NILT method is based on the approximation of the inverse kernel of the Laplace transform Bromwich integral exp(st). It is shown that with the use of the convergence accelerating algorithms onto the essence of the proposed NILT method, an enhancement on the core of the inversion is achieved, with relatively accurate and stable results, while preserving valuable time and memory. The algorithms are tested and their corresponding results are discussed, mainly regarding the accuracy, stability and computational efficiency. The experimental accuracy analysis tests are implemented in the universal MATLAB language with properly chosen Laplace transforms.
An iterative numerical technique for the evaluation of queue length distributions is applied to multi-queue systems with one server and cyclic service discipline with Bernoulli schedules. The technique is based on pow...
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Laplace transform analysis of electromagnetic power system transients generally is based on a technique in which the Laplace inversion integral is truncated with a suitable data window. This technique, being referred ...
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Laplace transform analysis of electromagnetic power system transients generally is based on a technique in which the Laplace inversion integral is truncated with a suitable data window. This technique, being referred to as WNLT, is appropriate for most practical cases. Nevertheless, it results inadequate for certain R&D tasks. This paper presents a new technique for numerical Laplace inversion that does not require truncation with a data window;it instead uses Brezinski's theta algorithm to account for the infinite range of the Laplace inversion integral. As opposed to the WNLT, the new technique guarantees consistent and high accuracy levels at low computational costs. Finally, the new technique is applied to the transient analysis of a power-system network. Its results compare favorably well with those from the PSCAD/EMTDC program.
A two-step strategy is proposed for the computation of singularities in nonlinear PDEs. The first step is the numerical solution of the PDE using a Fourier spectral method;the second step involves numerical analytical...
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A two-step strategy is proposed for the computation of singularities in nonlinear PDEs. The first step is the numerical solution of the PDE using a Fourier spectral method;the second step involves numerical analytical continuation into the complex plane using the epsilon algorithm to sum the Fourier series. Test examples include the inviscid Burgers and nonlinear heat equations as well as a transport equation involving the Hilbert transform. Numerical results, including Web animations that show the dynamics of the singularities in the complex plane, are presented.
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