Truncation Error Bounds for Continued Fractions $K({{a_n } / 1})$ with Parabolic Element Regions

1983 ◽  
Vol 20 (6) ◽  
pp. 1219-1230 ◽  
Author(s):  
William B. Jones ◽  
W. J. Thron ◽  
Haakon Waadeland
Keyword(s):  
Error Bounds ◽  
Continued Fractions ◽  
Truncation Error ◽  
Parabolic Element

Error Bounds of Continued Fractions for Complex Transport Coefficients and Spectral Functions

1978 ◽  
Vol 33 (11) ◽  
pp. 1380-1382 ◽  
Author(s):  
P. Hänggi
Keyword(s):  
Error Bounds ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Truncation Error ◽  
Transport Coefficients ◽  
Power Spectra ◽  
A Posteriori ◽  
Spectral Functions ◽  
Dynamical Equilibrium ◽  
Complex Continued Fractions

We study the calculation of complex transport coefficients x (ω) and power spectra in terms of complex continued fractions. In particular, we establish classes of dynamical equilibrium and non-equilibrium systems for which we can obtain a posteriori bounds for the truncation error | x (ω) - x(n)(ω)| ≦ c (ω) | x(n)(ω) - x(n-1)(ω)| when the transport coefficient is approximated by its n-th continued fraction approximant x(n)(ω).

Truncation Error Bounds for Continued Fractions

1969 ◽  
Vol 6 (2) ◽  
pp. 210-221 ◽  
Author(s):  
William B. Jones ◽  
R. I. Snell
Keyword(s):  
Error Bounds ◽  
Continued Fractions ◽  
Truncation Error

scholarly journals DISCRETE LAPLACE–BELTRAMI OPERATOR ON SPHERE AND OPTIMAL SPHERICAL TRIANGULATIONS

2006 ◽  
Vol 16 (01) ◽  
pp. 75-93 ◽  
Author(s):  
GUOLIANG XU
Keyword(s):  
Error Bounds ◽  
Truncation Error ◽  
Beltrami Operator ◽  
Discrete Operator ◽  
Convergence Properties

In this paper we first modify a widely used discrete Laplace-Beltrami operator proposed by Meyer et al over triangular surfaces, and then we show that the modified discrete operator has some convergence properties over the triangulated spheres. A sequence of spherical triangulations which is optimal in certain sense and leads to smaller truncation error of the discrete Laplace-Beltrami operator is constructed. Optimal hierarchical spherical triangulations are also given. Truncation error bounds of the discrete Laplace-Beltrami operator over the constructed triangulations are provided.

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