scholarly journals Piecewise Rational Quadratic Interpolation to Monotonic Data

1982 ◽  
Vol 2 (2) ◽  
pp. 123-130 ◽  
Author(s):  
J. A. GREGORY ◽  
R. DELBOURGO
Keyword(s):  
Quadratic Interpolation

Coupled electrical and thermal transient conduction problems with a quadratic interpolation cell method approach

2006 ◽  
Vol 42 (4) ◽  
pp. 1003-1006 ◽  
Author(s):  
M. Bullo ◽  
V. D'Ambrosio ◽  
F. Dughiero ◽  
M. Guarnieri
Keyword(s):  
Cell Method ◽  
Quadratic Interpolation ◽  
Transient Conduction ◽  
Thermal Transient ◽  
Method Approach

scholarly journals Approximation and application of the Riesz-Caputo fractional derivative of variable order with fixed memory

Meccanica ◽  
2021 ◽  
Author(s):  
Tomasz Blaszczyk ◽  
Krzysztof Bekus ◽  
Krzysztof Szajek ◽  
Wojciech Sumelka
Keyword(s):  
Differential Operator ◽  
Fractional Derivative ◽  
Rate Of Convergence ◽  
Continuum Mechanics ◽  
Caputo Fractional Derivative ◽  
Polynomial Interpolation ◽  
Piecewise Linear ◽  
Variable Order ◽  
Piecewise Constant ◽  
Quadratic Interpolation

AbstractIn this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods are based on polynomial interpolation: piecewise constant, piecewise linear, and piecewise quadratic interpolation. The errors generated by the described methods and the experimental rate of convergence are reported. Finally, an application of the Riesz-Caputo fractional derivative of space-dependent order in continuum mechanics is depicted.

Mathematical Modelling the Power Supply-Load System for Electro-Discharge Polishing Process

2010 ◽  
Vol 159 ◽  
pp. 125-128
Author(s):  
A. Parshuta ◽  
V. Chitanov ◽  
Lilyana Kolaklieva ◽  
Roumen Kakanakov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Power Supply ◽  
Equation System ◽  
Electrolyte Temperature ◽  
Polishing Process ◽  
The Real ◽  
Quadratic Interpolation ◽  
Runge Kutta

The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.

Parameterize the Center of the Trust Region for Solving Quadratic Interpolation Models

2011 ◽  
Vol 52-54 ◽  
pp. 920-925
Author(s):  
Qing Hua Zhou ◽  
Yan Geng ◽  
Ya Rui Zhang ◽  
Feng Xia Xu
Keyword(s):  
Optimization Problems ◽  
Trust Region Method ◽  
Main Idea ◽  
Trust Region ◽  
Search Region ◽  
Trust Region Algorithm ◽  
Unconstrained Optimization Problems ◽  
Simplex Search ◽  
Quadratic Interpolation ◽  
Derivative Free

The derivative free trust region algorithm was considered for solving the unconstrained optimization problems. This paper introduces a novel methodology that modified the center of the trust region in order to improve the search region. The main idea is parameterizing the center of the trust region based on the ideas of multi-directional search and simplex search algorithms. The scope of the new region was so expanded by introducing a parameter as to we can find a better descent directions. Experimental results reveal that the new method is more effective than the classic trust region method on the testing problems.

scholarly journals ANALYSIS OF MARKET VOLATILITY VIA A DYNAMICALLY PURIFIED OPTION PRICE PROCESS

2014 ◽  
Vol 09 (03) ◽  
pp. 1450006 ◽  
Author(s):  
CHUONG LUONG ◽  
NIKOLAI DOKUCHAEV
Keyword(s):  
Stock Price ◽  
Implied Volatility ◽  
Financial Time Series ◽  
Option Price ◽  
Option Prices ◽  
Price Process ◽  
Volatility Index ◽  
Quadratic Interpolation ◽  
Dynamic Estimation ◽  
The Impact

The paper studies methods of dynamic estimation of volatility for financial time series. We suggest to estimate the volatility as the implied volatility inferred from some artificial "dynamically purified" price process that in theory allows to eliminate the impact of the stock price movements. The complete elimination would be possible if the option prices were available for continuous sets of strike prices and expiration times. In practice, we have to use only finite sets of available prices. We discuss the construction of this process from the available option prices using different methods. In order to overcome the incompleteness of the available option prices, we suggests several interpolation approaches, including the first order Taylor series extrapolation and quadratic interpolation. We examine the potential of the implied volatility derived from this proposed process for forecasting of the future volatility, in comparison with the traditional implied volatility process such as the volatility index VIX.

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