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Miodrag S. Petkovi 'c Carsten Carstensen Miroslav Trajkov ' i c 《Numerische Mathematik》1995,69(3):353-372
Summary.
Classical Weierstrass' formula
[29] has been often the subject of investigation of many
authors. In this paper we give some further
applications of this formula for finding the zeros of polynomials and
analytic functions. We are concerned with the problems of
localization of polynomial zeros and the construction of iterative methods for
the simultaneous approximation and inclusion of these zeros.
Conditions for the safe convergence of Weierstrass' method,
depending only on initial approximations, are given. In particular,
we study polynomials with interval coefficients. Using an interval
version of Weierstrass' method enclosures in the form of disks
for the complex-valued set containing all zeros of a
polynomial with varying coefficients are obtained. We also present
Weierstrass-like algorithm for approximating, simultaneously, all
zeros of a class of analytic functions in a given closed region.
To demonstrate the proposed algorithms, three numerical
examples are included.
Received September 13, 1993 相似文献
2.
We present beam solutions of the strongly nonlocal nonlinear Schrödinger equation in left-handed materials (LHMs). Different Laguerre-Gaussian (LG) necklace beams, such as symmetric and asymmetric single layer and multilayernecklace beams are created by the superposition of two single beams with different topological charges. Such superpositions are then propagated through LHMs, displaying linear diffraction. It is found that the superposition of two LGnm beams with opposite topological charges does not show rotational behavior and that there exists rotation for other topological charge combinations. Our theory predicts that the accessible solitons cannot exist in LHMs. 相似文献
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