Comparative Study of Numerical Methods for Solving Non-linear Equations Using Manual Computation
Isaac Azure,
Golbert Aloliga,
Louis Doabil
Issue:
Volume 5, Issue 4, December 2019
Pages:
41-46
Received:
30 June 2019
Accepted:
25 December 2019
Published:
8 January 2020
Abstract: This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a root - finding problem manually with the help of an TI - inspire instrument. The outcome of the computations showed that all methods converged to an exact root of 1.56155, however the Bisection method converged at the 14th iteration, Fixed Point Iterative Method converged at 7th iteration, Secant method converged at the 5th iteration and Regula Falsi and Newton Raphson methods converged at the 2nd iteration, suggesting that Newton Raphson and Regula Falsi methods are more efficient in computing the roots of a nonlinear quadratic equation.
Abstract: This paper aims at comparing the performance in relation to the rate of convergence of five numerical methods namely, the Bisection method, Newton Raphson method, Regula Falsi method, Secant method, and Fixed Point Iteration method. A manual computational algorithm is developed for each of the methods and each one of them is employed to solve a roo...
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A Proposed New Model for Denton Proportional Method Generalization in Quarterly Disaggregation of the Gross Domestic Product
Raïmi Aboudou Essessino,
Guy Degla
Issue:
Volume 5, Issue 4, December 2019
Pages:
47-53
Received:
26 December 2019
Accepted:
8 January 2020
Published:
21 January 2020
Abstract: The estimation of a quarterly Gross Domestic Product (GDP) using an indirect approach based on quarterly indicators is often done by quarterly disaggregation of the national accounts branch per branch. The proportional method proposed by Denton (1971) leads to solving several optimization programs and doesn’t take into account the links between branches when searching for a quarterly GDP through indirect approach. This paper proposes a brand new approach to quarterly disaggregation of a GDP broken down into several branches or sectors, that takes into account the links between this branches. This approach generalizes the Denton (1971) proportional method and is an integrated approach in which the quarterly disaggregation of GDP is formulated as a multiobjective optimization problem. In fact, we group together on the one hand, all the elementary objective functions identified with respect to the various branches, and on the other hand, all the prescribed constraints according to the branches. Our technique relies on the minimization (in the least squares sense) of the difference in adjustment from neighbouring quarters under constraints provided by the annual benchmark data. The proposed model can be applied to the national accounts of any country using any approach for GDP compilation and it also takes also into account the usual inter dependence of its branches lacking in Denton method. Besides, it is worth noting that an algorithmic method needs to be devised due to the large scale of concrete GDP disaggregation problems.
Abstract: The estimation of a quarterly Gross Domestic Product (GDP) using an indirect approach based on quarterly indicators is often done by quarterly disaggregation of the national accounts branch per branch. The proportional method proposed by Denton (1971) leads to solving several optimization programs and doesn’t take into account the links between bra...
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