On the global convergence of Schröder’s iteration formula for real zeros of entire functions

2019 ◽  
Vol 358 ◽  
pp. 136-145
Author(s):  
Hiroshi Sugiura ◽  
Takemitsu Hasegawa
Keyword(s):  
Global Convergence ◽  
Entire Functions ◽  
Real Zeros ◽  
Iteration Formula ◽  
Zeros Of Entire Functions

The phase problem in scattering phenomena: the zeros of entire functions and their significance

1978 ◽  
Vol 360 (1700) ◽  
pp. 25-45 ◽  
Keyword(s):  
Entire Functions ◽  
Signal To Noise Ratio ◽  
Phase Problem ◽  
Distribution Of Zeros ◽  
Real Zeros ◽  
Zeros Of Entire Functions ◽  
Functions Of Exponential Type ◽  
Zeros Of Functions ◽  
The Fourier Transform ◽  
Complex Zeros

The paper outlines an approach to the calculation of the phase from intensity data based on the properties of the distribution of zeros of functions of exponential type. This leads to a reinterpretation of such phenomena as Gibbs’ or speckle, which underlines their intrinsic unity. The phase problem is solved for functions which present complex zeros by apodization, i.e. by creating a sufficiently large zero-free area. The method is based on a compromise between signal to noise ratio and resolution and is meaningful provided the apodization required is not too severe. Real zeros, for which the phase problem is trivial, occur only for the special case of eigenfunctions of the Fourier transform

On the global convergence of Halley's iteration formula

1975 ◽  
Vol 24 (2) ◽  
pp. 133-135 ◽  
Author(s):  
M. Davies ◽  
B. Dawson
Keyword(s):  
Global Convergence ◽  
Iteration Formula
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