A new method for finding the largest eigenvalue of a generalised nonnegative polynomial was introduced in 2014 by Ibrahim. The method was proven to be convergent for weakly irreducible polynomials. In the method, an irreducible polynomial is shifted such that it becomes primitive. However, it is illlkno\Vll what is the optimal shift and the effect of the step length to the method. In this study we examine the effect of the step leugtli to tlie metliod...

344 hits

In this paper, we present the distribution of some maximal eigenvalues that are obtained numerically from the discrete Dirichlet Boundary Domain Integro-Dierential Equation (BDIDE) operator. We also discuss the convergence of the discrete Dirichlet BDIDE that corresponds with the obtained absolute value of the largest eigenvalues of the discrete BDIDE operator. There are three test domains that are considered in this paper, i.e., a square, a circle, and a parallelogram. In our numerical test, the eigenvalues disperse as the power of the variable coecient increases. Not only that, we also note that the dispersion of the eigenvalues corresponds with the characteristic size of the test domains. It enables us to predict the convergence of an iterative method. This is an advantage as it enables the use of an iterative method in solving Dirichlet BDIDE as an alternative to the direct methods  ..

374 hits

The conjugate gradient method is one of the best methods that can be used to solve nonlinear unconstrained optimization problems. This method has gained the interest of researchers and has expanded rapidly. There are many versions of the conjugate gradient method. Each version claims to be ecient. In this paper, we make the comparison among three versions of the conjugate gradient method (MRM, SRMI and BZAU) by using exact line search. The methods were tested in terms of number of iteration and CPU time using 20 standard test functions. The result showed that MRM is the most ecient followed by BZAU and then SRMI. However, BZAU successfully found all the minimizers of the test functions whereas both SRMI and MRM failed at least once. In order to test the robustness of the methods, extensive tests are required.  ..

538 hits

The purposes of this study are to determine the ratio of instantaneous speed on Federal highway at Kilometer 32.9 from Kuala Lumpur to Shah Alam, to analyse the implications of the instantaneous speed ratio's numerical findings, and to examine the behaviour of convergence for each level of easiness to flow. The continuous flow model is one of the traffic flow theories that conclude the traffic flow is identical to the equation of heat. The research design used in this study is a comparative model. The continuous flow model uses a boundary value problem as well as additional constraints to solve the differential equation solution. The videotaping approach was used to select a sample of highway traffic data on the tapered acceleration path. The findings of this study disclosed that the ratio of instantaneous speed converged slower at lower levels of easiness to flow than at higher levels of easiness to flow. The ratio of instantaneous speed was found to be more accurate when the addition.....

276 hits

Most integrals in Localised Boundary Domain Integral Equations (LBDIEs) comprise singularities. This paper aims to produce numerical solutions of the LBDIEs for the Partial Differential Equations with variable coefficients. The singularities of the boundary integrals in LBDIEs will be handled by using a semi-analytic for logarithmic singularity and a semi-quadratic analytic method for r?2 singularity. Whereas the singular domain integrals are handled by using the Duffy transformation. The LBDIEs that we consider are associated with the Neumann problem, which can be solved with a condition. If it can be solved, the solution is, however, unique up to an additive constant. We add a perturbation operator to the LBDIEs to convert the LBDIE to a uniquely solvable equation. The perturbed integral operator leads the perturbed LBDIEs to a dense matrix system that disable the use of methods in solving sparse matrix system. We solve the system of linear equations by Lower-Upper (LU) decomposition.....

96 hits

This paper focuses on modifying the existing Conjugate Gradient (CG) method of Rivaie, Mustafa, Ismail and Leong (RMIL). The RMIL technique has been the subject of previous studies to enhance its effectiveness. In this study, a new CG search direction, IRMIL, has been presented. This new variation combines the scaled negative gradient, which acts as an initial direction, and a third-term parameter. This paper proves that the IRMIL satisfies the sufficient descent criteria. The method also exhibits global convergence characteristics for exact and strong Wolfe line searches. The methods efficacy is assessed using two distinct methodologies. The first methodology involved conducting numerical tests on conventional Unconstrained Optimisation (UO) problems. The test shows that, while the IRMIL method performs very similarly to other existing CG methods during exact line search, it excels during strong Wolfe line search and converges more quickly. For the second methodology, the NEWMRIL meth.....

110 hits