Best a Posteriori Truncation Error Estimates for Continued Fractions K(an/1) with Twin Element Regions

1988 ◽  
pp. 335-347
Author(s):  
William B. Jones ◽  
Walter M. Reid
Keyword(s):  
Error Estimates ◽  
Continued Fractions ◽  
Truncation Error ◽  
A Posteriori

A Posteriori Bounds for the Truncation Error of Continued Fractions

1971 ◽  
Vol 8 (4) ◽  
pp. 693-705 ◽  
Author(s):  
William B. Jones ◽  
W. J. Thron
Keyword(s):  
Continued Fractions ◽  
Truncation Error ◽  
A Posteriori

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).

scholarly journals Regularization of backward time-fractional parabolic equations by Sobolev-type equations

2020 ◽  
Vol 28 (5) ◽  
pp. 659-676
Author(s):  
Dinh Nho Hào ◽  
Nguyen Van Duc ◽  
Nguyen Van Thang ◽  
Nguyen Trung Thành
Keyword(s):  
Error Estimates ◽  
Parabolic Equations ◽  
Regularization Parameter ◽  
A Priori ◽  
Sobolev Type ◽  
A Posteriori ◽  
Parameter Choice ◽  
Numerical Tests ◽  
Ill Posed ◽  
Parameter Choice Rules

AbstractThe problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable noniterative numerical scheme. The theoretical error estimates are confirmed by numerical tests for one- and two-dimensional equations.

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