scholarly journals Convergence Analysis of a Modified Weierstrass Method for the Simultaneous Determination of Polynomial Zeros

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1408
Author(s):  
Plamena I. Marcheva ◽  
Stoil I. Ivanov
Keyword(s):  
Error Estimate ◽  
Convergence Analysis ◽  
Simultaneous Determination ◽  
Numerical Experiments ◽  
Practical Importance ◽  
Semilocal Convergence ◽  
Numerical Comparison ◽  
Initial Condition ◽  
Polynomial Zeros

In 2016, Nedzhibov constructed a modification of the Weierstrass method for simultaneous computation of polynomial zeros. In this work, we obtain local and semilocal convergence theorems that improve and complement the previous results about this method. The semilocal result is of significant practical importance because of its computationally verifiable initial condition and error estimate. Numerical experiments to show the applicability of our semilocal theorem are also presented. We finish this study with a theoretical and numerical comparison between the modified Weierstrass method and the classical Weierstrass method.

scholarly journals Semilocal Convergence Theorem for the Inverse-Free Jarratt Method under New Hölder Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yueqing Zhao ◽  
Rongfei Lin ◽  
Zdenek Šmarda ◽  
Yasir Khan ◽  
Jinbiao Chen ◽  
...  
Keyword(s):  
Banach Space ◽  
Error Estimate ◽  
Convergence Analysis ◽  
Operator Equation ◽  
Convergence Theorem ◽  
Nonlinear Operator ◽  
Semilocal Convergence ◽  
Nonlinear Operator Equation ◽  
Jarratt Method ◽  
Semilocal Convergence Theorem

Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.

scholarly journals Дослідження напруженого стану міжпазових виступів диска робочого колеса компресора з урахуванням впливу відцентрових сил та розладу частот коливань лопаток

2021 ◽  
pp. 47-54
Author(s):  
Анатолій Павлович Зіньковський ◽  
Вячеслав Михайлович Меркулов ◽  
Олег Леонідович Деркач ◽  
Іван Гордійович Токар ◽  
Кирило Валентинович Савченко
Keyword(s):  
Stress State ◽  
Gas Turbine ◽  
Numerical Experiments ◽  
Practical Importance ◽  
Gas Turbine Engine ◽  
Full Scale ◽  
Centrifugal Forces ◽  
Blade Vibration ◽  
Turbine Engine

The authors present the results of the numerical experiments on the determination of the effect of compressor blade mistuning on the stress state of a blade-disk joint under the action of the centrifugal forces and their comparison with results of full-scale experiments. The analysis of the results of the previously performed experimental and numerical experiments on the determination of the possible sources of blade-disk joints failure shows their stress state strongly depends on the disk rim thickness and the blade vibration mode and their mistuning. It indicates the need for further studies to determine the causes of cracks and possible fracture of blade-disk joints in the compressor of a gas-turbine engine. The task is solved in the variation of the dovetail-rim region thickness of the disk of the 1st stage of the low-pressure compressor of the gas-turbine engine D-36, which has blades without shrouds. The finite element models of the blade assembly, are used to perform the investigation. Obtained results of the vibration stress analysis of blade-disk joints in the compressor both modifications under the action of the centrifugal forces have good agreement with the data of full-scale experiments and numerical data using rod models. The presented results of the numerical experiments indicate the possibility of reducing vibration stresses by analyzing and choosing parameters that affect the rigidity of the coupling of the blades, which is of practical importance for increasing the vibration reliability of the compressors of gas-turbine engines.

On some methods for the simultaneous determination of polynomial zeros

1996 ◽  
Vol 13 (2) ◽  
pp. 267-288 ◽  
Author(s):  
Sachio Kanno ◽  
Nikolai V. Kjurkchiev ◽  
Tetsuro Yamamoto
Keyword(s):  
Simultaneous Determination ◽  
Polynomial Zeros

A general computer program for the extended plate overlap algorithm

1978 ◽  
Vol 48 ◽  
pp. 287-293 ◽  
Author(s):  
Chr. de Vegt ◽  
E. Ebner ◽  
K. von der Heide
Keyword(s):  
Computer Program ◽  
Simultaneous Determination ◽  
General Computer Program ◽  
General Computer

In contrast to the adjustment of single plates a block adjustment is a simultaneous determination of all unknowns associated with many overlapping plates (star positions and plate constants etc. ) by one large adjustment. This plate overlap technique was introduced by Eichhorn and reviewed by Googe et. al. The author now has developed a set of computer programmes which allows the adjustment of any set of contemporaneous overlapping plates. There is in principle no limit for the number of plates, the number of stars, the number of individual plate constants for each plate, and for the overlapping factor.

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