An iterative algorithm for computing the eigenvalues of spherical hybrid modes in corrugated conical horns with arbitrary corrugation depth is presented. The eigenvalue equation is expressed in terms of definite integ...
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An iterative algorithm for computing the eigenvalues of spherical hybrid modes in corrugated conical horns with arbitrary corrugation depth is presented. The eigenvalue equation is expressed in terms of definite integrals and the eigenvalues appear as constants associated with the integrands. The Newton-Raphson iteration technique is used for evaluating the eigenvalues. Starting values needed for the iteration are supplied through an asymptotic solution for eigenvalues, available in closed form and valid over a wide range of semiflare angle (0 < α0 ≤ 90°) of the horn. A computer program is available for calculating eigenvalues of the HE11 mode in horns with arbitrary corrugation depth (0.25 ≤ h/λ ≤ 0.50).
With the increasing availability of high-speed multiplication units in large computers it is attractive to develop an iterative procedure to compute division and square root, using multiplication as the primary operat...
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With the increasing availability of high-speed multiplication units in large computers it is attractive to develop an iterative procedure to compute division and square root, using multiplication as the primary operation. In this paper, we present three new methods of performing square rooting rapidly which utilize multiplication and no division. Each algorithm is considered for convergence rate, efficiency, and implementation. The most typical and efficient one of the already-known algorithms which utilizes multiplication, here called the N algorithm, is introduced for the purpose of comparison with the new algorithms. The effect and importance of the initial approximation is considered. (One of the algorithms, here called the G algorithm, is described in detail with the emphasis on its high efficiency.)
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