scholarly journals On a Pointwise Convergence of Quasi-Periodic-Rational Trigonometric Interpolation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Arnak Poghosyan ◽  
Lusine Poghosyan
Keyword(s):  
Pointwise Convergence ◽  
Convergence Acceleration ◽  
Trigonometric Interpolation ◽  
Special Choice ◽  
Unknown Parameters ◽  
Exact Constants

We introduce a procedure for convergence acceleration of the quasi-periodic trigonometric interpolation by application of rational corrections which leads to quasi-periodic-rational trigonometric interpolation. Rational corrections contain unknown parameters whose determination is important for realization of interpolation. We investigate the pointwise convergence of the resultant interpolation for special choice of the unknown parameters and derive the exact constants of the main terms of asymptotic errors.

scholarly journals Optimal Rational Approximations by the Modified Fourier Basis

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Arnak V. Poghosyan ◽  
Tigran K. Bakaryan
Keyword(s):  
Numerical Experiments ◽  
Pointwise Convergence ◽  
Convergence Acceleration ◽  
Rational Approximations ◽  
Unknown Parameters ◽  
Fourier Basis ◽  
Optimal Values ◽  
Exact Constants ◽  
Selection Of

We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis.

FOURIER FORMULAE FOR EQUIDISTANT HERMITE TRIGONOMETRIC INTERPOLATION

2011 ◽  
Vol 04 (01) ◽  
pp. 127-144 ◽  
Author(s):  
Arnak Poghosyan
Keyword(s):  
Convergence Acceleration ◽  
Lanczos Method ◽  
Trigonometric Interpolation ◽  
Quadrature Formulae ◽  
Interpolation Polynomials ◽  
Exact Constants ◽  
Interpolation Nodes

A sequence of Hermite trigonometric interpolation polynomials with equidistant interpolation nodes and uniform multiplicities is investigated. We derive relatively compact formula that gives the interpolants as functions of the coefficients in the DFTs of the derivative values. The coefficients can be calculated by the FFT algorithm. Corresponding quadrature formulae are derived and explored. Convergence acceleration based on the Krylov-Lanczos method for accelerating both the convergence of interpolation and quadrature is considered. Exact constants of the asymptotic errors are obtained and some numerical illustrations are presented.

scholarly journals On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Arnak Poghosyan
Keyword(s):  
Trigonometric Polynomial ◽  
Numerical Experiments ◽  
Polynomial Interpolation ◽  
Convergence Acceleration ◽  
Fast Convergence ◽  
Exact Constants

We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to the Krylov-Lanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.

CONVERGENCE ACCELERATION OF INTEGRAL TRANSFORM SOLUTIONS

2001 ◽  
Vol 3 (1) ◽  
pp. 6
Author(s):  
Mikhail D. Mikhailov ◽  
Renato M. Cotta
Keyword(s):  
Integral Transform ◽  
Convergence Acceleration

Graphic method for assessing the margins of resistance to acoustic vibrations in the chambers of rocket engines by combustion noise

2020 ◽  
pp. 15-21
Author(s):  
R.A. Tsarapkin ◽  
V.N. Ivanov ◽  
V.I. Biryukov
Keyword(s):  
Rocket Engine ◽  
Spectral Characteristics ◽  
Combustion Process ◽  
Combustion Noise ◽  
Rocket Engines ◽  
Acoustic Vibrations ◽  
Statistical Regression ◽  
Unknown Parameters ◽  
Damping Decrement ◽  
Resonance Frequencies

An experimental method is proposed for estimating the damping decrements of pressure fluctuations in the combustion chambers of forced rocket engines. The method is based on the statistical processing of noise pressure pulsations in the vicinity of natural resonance frequencies for normal modes of acoustic vibrations of the reaction volume and the subsequent prediction of the instability of the combustion process relative to acoustic vibrations. Based on the theory of statistical regression for multidimensional experimental data, the problem of predicting unknown parameters of sample distributions is solved by asymptotic determination of the correlation coefficient of the damping decrement of pressure vibrations through optimal linear predictors and the Kolmogorov distribution. Keywords rocket engine, combustion chamber, acoustic vibrations, combustion noise, spectral characteristics, Kolmogorov criterion, damping decrement. [email protected]

SPACE SURVEILLANCE SYSTEM’S SAR SIGNAL DETECTION RESULTS

2018 ◽  
pp. 63-68 ◽  
Author(s):  
A. V. Ksendzuk ◽  
A. A. Kanatchikov ◽  
P. A. Gerasimov
Keyword(s):  
Signal Detection ◽  
Surveillance System ◽  
Observation Interval ◽  
Pulse Repetition Frequency ◽  
Storage Device ◽  
Periodic Signal ◽  
Unknown Parameters ◽  
Software Optimization ◽  
Space Objects ◽  
Field Programmable

Special aspects of space objects radiotechnical surveillance system used for filling the space tracking and surveillance system (STSS) satellite catalogue described and analyzed. Special emphasis placed on spaceborne synthetic aperture radar signals detection. Parameters of the SAR signals estimated with the proposed radiotechnical surveillance system described. Two processing methods for unknown and partially known signals proposed and analyzed. Signal detection with incompletely known parameters performs with cumulative second-order statistic. Signal detection with unknown parameters performs for periodic signal in assumption that observation interval exceed pulse repetition frequency. Proposed methods implemented in hardware demonstrator of radiotechnical surveillance system. This demonstrator works in real-time on Field Programmable Gate Array or save data on storage device for post-processing. L-band Palsar2 signal detection results presented and analyzed. Further work for hardware and software optimization described.

An experimental method for evaluating constitutive models of myocardium in in vivo hearts

1994 ◽  
Vol 267 (2) ◽  
pp. H853-H863 ◽  
Author(s):  
L. L. Creswell ◽  
M. J. Moulton ◽  
S. G. Wyers ◽  
J. S. Pirolo ◽  
D. S. Fishman ◽  
...  
Keyword(s):  
Experimental Method ◽  
Diastolic Pressure ◽  
Constitutive Models ◽  
Fe Analysis ◽  
Small Displacement ◽  
Ventricular Wall ◽  
Canine Heart ◽  
Unknown Parameters ◽  
Tissue Tagging

A new experimental method for the evaluation of myocardial constitutive models combines magnetic resonance (MR) radiofrequency (RF) tissue-tagging techniques with iterative two-dimensional (2-D) nonlinear finite element (FE) analysis. For demonstration, a nonlinear isotropic constitutive model for passive diastolic expansion in the in vivo canine heart is evaluated. A 2-D early diastolic FE mesh was constructed with loading parameters for the ventricular chambers taken from mean early diastolic-to-late diastolic pressure changes measured during MR imaging. FE solution was performed for regional, intramyocardial ventricular wall strains using small-strain, small-displacement theory. Corresponding regional ventricular wall strains were computed independently using MR images that incorporated RF tissue tagging. Two unknown parameters were determined for an exponential strain energy function that maximized agreement between observed (from MR) and predicted (from FE analysis) regional wall strains. Extension of this methodology will provide a framework in which to evaluate the quality of myocardial constitutive models of arbitrary complexity on a regional basis.

scholarly journals Adaptive Control of a Vehicular Platoon with Unknown Parameters and Input Variations

2020 ◽  
Vol 53 (2) ◽  
pp. 13876-13881
Author(s):  
Mohammad Pourmahmood Aghababa ◽  
Mehrdad Saif ◽  
Bahram Shafai
Keyword(s):  
Adaptive Control ◽  
Unknown Parameters
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