Current Issue : April - June Volume : 2013 Issue Number : 2 Articles : 4 Articles
For ordinal log-linear models, the estimation of the parameter reflecting the linear-by-linear measure of association has long been\r\na topic for the analysis of dependence for contingency tables. Typically, iterative procedures (including Newtonââ?¬â?¢s method) are used\r\nto determine the maximum likelihood estimate of the parameter. Recently Beh and Farver (2009, ANZJS, 51, 335ââ?¬â??352) show by\r\nway of example three reliable and accurate noniterative techniques that can be used to estimate the parameter and extended this\r\nstudy by examining their reliability computationally. This paper further investigates the reliability of the non-iterative procedures\r\nwhen compared with Newtonââ?¬â?¢s method for estimating this association parameter and considers the impact of the sample size on\r\nthe estimate....
We propose a conjugate gradient method which is based on the study of the Dai-Liao conjugate gradient method. An important\r\nproperty of our proposed method is that it ensures sufficient descent independent of the accuracy of the line search. Moreover, it\r\nachieves a high-order accuracy in approximating the second-order curvature information of the objective function by utilizing the\r\nmodified secant condition proposed by Babaie-Kafaki et al. (2010). Under mild conditions, we establish that the proposed method\r\nis globally convergent for general functions provided that the line search satisfies theWolfe conditions. Numerical experiments are\r\nalso presented....
This paper considers the nonlinear boundary value problem (BVP) for the electrohydrodynamic flow of a fluid in an ion drag\r\nconfiguration in a circular cylindrical conduit. The velocity field was solved using the new homotopy perturbation method\r\n(NHPM), considering the electrical field and strength of the nonlinearity. The approximate analytical procedure depends only\r\non two components and polynomial initial condition. The analytical solution is obtained and the numerical results presented\r\ngraphically. The effects of the Hartmann electric number Ha and the strength of nonlinearity a are discussed and presented\r\ngraphically.We also compare this method with numerical solution (N.S) and show that the present approach is less computational\r\nand is applicable for solving nonlinear boundary value problem (BVP)....
Estimating linear-by-linear association has long been an important topic in the analysis of contingency tables. For ordinal variables,\r\nlog-linear models may be used to detect the strength and magnitude of the association between such variables, and iterative\r\nprocedures are traditionally used. Recently, studies have shown, by way of example, three non-iterative techniques can be used\r\nto quickly and accurately estimate the parameter. This paper provides a computational study of these procedures, and the results\r\nshow that they are extremely accurate when compared with estimates obtained using Newton�s unidimensional method....
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