Properties of Padé approximants to stieltjes series and systems theory

1984 ◽  
pp. 182-188
Author(s):  
N. K. Bose
Keyword(s):  
Systems Theory ◽  
Padé Approximants ◽  
Pade Approximants ◽  
Stieltjes Series

Two-point Padé approximants for formal Stieltjes series

1994 ◽  
Vol 8 (2) ◽  
pp. 313-328 ◽  
Author(s):  
Stanisław Tokarzewski ◽  
Jerzy Bławzdziewicz ◽  
Igor Andrianov
Keyword(s):  
Padé Approximants ◽  
Pade Approximants ◽  
Stieltjes Series

Padé approximants of random Stieltjes series

2007 ◽  
Vol 463 (2087) ◽  
pp. 2813-2832
Author(s):  
Jens Marklof ◽  
Yves Tourigny ◽  
Lech Wołowski
Keyword(s):  
Continued Fraction ◽  
Bessel Functions ◽  
Padé Approximants ◽  
Independent Random Variables ◽  
Disordered System ◽  
One Dimensional ◽  
Pade Approximants ◽  
Explicit Formulae ◽  
Stieltjes Series ◽  
Positive Half

We consider the random continued fraction where s n are independent random variables with the same gamma distribution. Every realization of the sequence defines a Stieltjes function that can be expressed as for some measure σ on the positive half-line. We study the convergence of the finite truncations of the continued fraction or, equivalently, of the diagonal Padé approximants of the function S . Using the Dyson–Schmidt method for an equivalent one-dimensional disordered system and the results of Marklof et al. , we obtain explicit formulae (in terms of modified Bessel functions) for the almost sure rate of convergence of these approximants, and for the almost sure distribution of their poles.

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