scholarly journals A truncation error bound for some branched continued fractions of the special form

2019 ◽  
Vol 52 (2) ◽  
Author(s):  
I. B. Bilanyk
Keyword(s):  
Error Bound ◽  
Continued Fractions ◽  
Special Form ◽  
Truncation Error

scholarly journals Generalization of Kravchenko—Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions

2019 ◽  
Vol 484 (4) ◽  
pp. 405-409
Author(s):  
K. A. Budunova ◽  
V. F. Kravchenko ◽  
V. I. Pustovoit
Keyword(s):  
Numerical Experiment ◽  
Error Bound ◽  
Special Form ◽  
Truncation Error ◽  
Infinite Product ◽  
Compactly Supported ◽  
Differentiable Functions ◽  
Infinitely Differentiable Functions ◽  
Linear Integral ◽  
Linear Integral Equations

New generalization of Kravchenko–Kotelnikov theorem by spectra of compactly supported infinitely differentiable functions is discussed. These functions are solutions of linear integral equations of special form. The spectrum of is a multiple infinite product of the spectra of atomic functions. dilated by the argument. Constructed generalized series has fast convergence. This property is confirmed by the presented truncation error bound formula and the results of a numerical experiment.

scholarly journals Some convergence regions of branched continued fractions of special form

2013 ◽  
Vol 5 (1) ◽  
pp. 4-13 ◽  
Author(s):  
O.E. Baran
Keyword(s):  
Continued Fractions ◽  
Special Form

Some circular and parabolic convergence regions for branched continued fractions of special form are established.

scholarly journals On the convergence criterion for branched continued fractions with independent variables

2018 ◽  
Vol 9 (2) ◽  
pp. 120-127 ◽  
Author(s):  
R.I. Dmytryshyn
Keyword(s):  
Power Series ◽  
Continued Fractions ◽  
Special Form ◽  
Absolute Convergence ◽  
Convergence Criterion ◽  
Complex Numbers ◽  
Independent Variables ◽  
Nonnegative Coefficients ◽  
Multiple Power ◽  
Multiple Power Series

In this paper, we consider the problem of convergence of an important type of multidimensional generalization of continued fractions, the branched continued fractions with independent variables. These fractions are an efficient apparatus for the approximation of multivariable functions, which are represented by multiple power series. We have established the effective criterion of absolute convergence of branched continued fractions of the special form in the case when the partial numerators are complex numbers and partial denominators are equal to one. This result is a multidimensional analog of the Worpitzky's criterion for continued fractions. We have investigated the polycircular domain of uniform convergence for multidimensional C-fractions with independent variables in the case of nonnegative coefficients of this fraction.

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

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

scholarly journals Positive definite branched continued fractions of special form

2013 ◽  
Vol 5 (2) ◽  
pp. 225-230
Author(s):  
R.I. Dmytryshyn
Keyword(s):  
Quadratic Form ◽  
Continued Fractions ◽  
Special Form ◽  
Positive Definite

Research of the class of branched continued fractions of special form, whose denominators do not equal to zero, is proposed and the connection of such fraction with a certain quadratic form is established. It furnishes new opportunities for the investigation of convergence of branching continued fractions of special form.

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