A survey of truncation error analysis for Pad� and continued fraction approximants

1993 ◽  
Vol 33 (2-3) ◽  
pp. 211-272 ◽  
Author(s):  
Cathleen Craviotto ◽  
William B. Jones ◽  
W. J. Thron
Keyword(s):  
Error Analysis ◽  
Continued Fraction ◽  
Truncation Error

Truncation Error Analysis on Reconstruction of Signal From Unsymmetrical Local Average Sampling

2015 ◽  
Vol 45 (10) ◽  
pp. 2100-2104 ◽  
Author(s):  
Yanwei Pang ◽  
Zhanjie Song ◽  
Xuelong Li ◽  
Jing Pan
Keyword(s):  
Error Analysis ◽  
Truncation Error ◽  
Average Sampling ◽  
Local Average

scholarly journals Truncation Error Analysis of Multipole Expansion

2004 ◽  
Vol 25 (4) ◽  
pp. 1293-1306 ◽  
Author(s):  
Shinichiro Ohnuki ◽  
Weng Cho Chew
Keyword(s):  
Error Analysis ◽  
Truncation Error ◽  
Multipole Expansion

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

2011 ◽  
Vol 19 (2) ◽  
Author(s):  
S. Sujecki
Keyword(s):  
Refractive Index ◽  
Finite Difference ◽  
Error Analysis ◽  
Optical Waveguides ◽  
Light Propagation ◽  
Truncation Error ◽  
Mesh Size ◽  
Refractive Index Profile ◽  
Finite Difference Approximations ◽  
Difference Approximations

AbstractA rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h2) truncation error only asymptotically for sufficiently small values of the mesh size.

scholarly journals Truncation error bounds for branched continued fraction whose partial denominators are equal to unity

2020 ◽  
Vol 54 (1) ◽  
pp. 3-14
Author(s):  
R. I. Dmytryshyn ◽  
T. M. Antonova
Keyword(s):  
Complex Plane ◽  
Error Bounds ◽  
Continued Fraction ◽  
Truncation Error ◽  
Independent Variables ◽  
Continued Fraction Expansions ◽  
Branched Continued Fraction

The paper deals with the problem of obtaining error bounds for branched continued fraction of the form $\sum_{i_1=1}^N\frac{a_{i(1)}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{a_{i(2)}}{1}{\atop+}\sum_{i_3=1}^{i_2}\frac{a_{i(3)}}{1}{\atop+}\ldots$. By means of fundamental inequalities method the truncation error bounds are obtained for the above mentioned branched continued fraction providing its elements belong to some rectangular sets ofa complex plane. Applications are considered for several classes of branched continued fraction expansions including the multidimensional \emph{S}-, \emph{A}-, \emph{J}-fractions with independent variables.

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