• Honam Mathematical Journal
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• v.35 no.3
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• pp.417-433
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• 2013

We consider the iterative solution of a quadratic matrix equation with special coefficient matrices which arises in the quasibirth and death problem. In this paper, we show that the elementwise minimal positive solvent of the quadratic matrix equations can be obtained using Newton's method if there exists a positive solvent and the convergence rate of the Newton iteration is quadratic if the Fr$\acute{e}$chet derivative at the elementwise minimal positive solvent is nonsingular. Although the Fr$\acute{e}$chet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.

• Journal of Animal Science and Technology
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• v.63 no.4
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• pp.827-840
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• 2021

Several studies have focused on Ca and P requirements for pigs. These requirements are estimated from their retention and bone formation. However, modern pig breeds have different responses to dietary Ca and P than traditional breeds, and their requirements are expected to change on an annual basis. Besides individual Ca and P needs, the Ca to P ratio (Ca/P) is an important factor in determining requirements. This study aimed to implement a linear and quadratic regression analysis to estimate Ca and P requirements based on average daily gain (ADG), apparent total tract digestibility (ATTD) of Ca (ATTD-Ca), ATTD of P (ATTD-P), and crude protein (CP) digestibility. Results show that Ca/P had linear and quadratic effects on ADG in the phytase-supplemented (PS) group in both the 6-11 kg and 11-25 kg categories. In the latter category, the CP digestibility was linearly increased in response to increasing Ca/P in the without-phytase (WP) group. In the 25-50 kg category, there was a linear response of ADG and linear and quadratic responses of CP digestibility to Ca/P in the PS group, while a linear and quadratic increase in CP digestibility and a quadratic effect on ATTD-Ca were observed in the WP group. In the 50-75 kg category, Ca/P had significant quadratic effects on ADG in the PS and WP groups, along with significant linear and quadratic effects on ATTD-Ca. In addition, Ca/P had significant quadratic effects on ATTD-P and led to a significant linear and quadratic increase in the CP digestibility in the WP group. In the 75-100 kg category, analysis showed a significant decrease in ATTD-Ca and ATTD-P in the PS and WP groups; in the latter, ATTD-P and ATTD-Ca were linearly decreased by increasing Ca/P. In conclusion, our equations predicted a higher Ca/P in the 6-25 kg bodyweight categories and a lower Ca/P in the 50-100 kg category than that recommended in the literature.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.823-835
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• 2010

In this paper, A FSQP algorithm for degenerate inequality constraints optimization problems is proposed. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving a quadratic programming subproblem. To overcome the Maratos effect, a higher-order correction direction is obtained by solving another quadratic programming subproblem. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions. Finally, some preliminary numerical results are reported.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.133-148
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• 2006

This paper proposes a smoothing method for symmetric conic linear programming (SCLP). We first characterize the central path conditions for SCLP problems with the help of Chen-Harker-Kanzow-Smale smoothing function. A smoothing-type algorithm is constructed based on this characterization and the global convergence and locally quadratic convergence for the proposed algorithm are demonstrated.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.239-251
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• 2007

We show how the minimization can be used to solve the quadratic matrix equation and then compare two different types of conjugate gradient method which are Polak and Ribi$\acute{e}$re version and Fletcher and Reeves version. Finally, some results of the global and local convergence are shown.

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.487-497
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• 2011

In this paper we propose a simple iterative method for finding a root of a nonlinear equation. It is shown that the new method, which does not require any derivatives, has a quadratic convergence order. In addition, one can find that a hybrid method combined with the non-iterative method can further improve the convergence rate. To show the efficiency of the presented method we give some numerical examples.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.399-409
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• 2008

We consider the most generalized quadratic matrix equation, Q(X) = $A_7XA_6XA_5+A_4XA_3+A_2XA_1+A_0=0$, where X is m ${\times}$ n, $A_7$, $A_4$ and $A_2$ are p ${\times}$ m, $A_6$ is n ${\times}$ m, $A_5$, $A_3$ and $A_l$ are n ${\times}$ q and $A_0$ is p ${\times}$ q matrices with complex elements. The convergence of Newton's method for solving some different types of quadratic matrix equations are considered and we show that the elementwise minimal positive solvents can be found by Newton's method with the zero starting matrices. We finally give numerical results.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1395-1407
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• 2011

When a Sequential Quadratic Programming (SQP) method is used to solve the nonlinear programming problems, one of the main difficulties is that the Quadratic Programming (QP) subproblem may be incompatible. In this paper, an SQP algorithm is given by modifying the traditional QP subproblem and applying a class of $l_{\infty}$ penalty function whose penalty parameters can be adjusted automatically. The new QP subproblem is compatible. Under the extended Mangasarian-Fromovitz constraint qualification condition and the boundedness of the iterates, the algorithm is showed to be globally convergent to a KKT point of the non-linear programming problem.

• Journal of Electrical Engineering and Technology
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• v.6 no.5
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• pp.626-633
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• 2011

This paper presents a novel maximum efficiency control scheme for convergence improvement in stator-flux-oriented induction motor drives. Three input powers are calculated at three different flux levels, respectively. A quadratic curve is obtained using the quadratic interpolation method using the three points. The flux level at the lowest point of the interpolated curve is calculated, which is not the real minimum input power of the motor, but an estimated one. Hence, the quadratic interpolations are repeated with three new points chosen using the selection method for new points for refitting until the convergence criteria are satisfied. The proposed method is verified by simulation results.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.199-214
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• 2017

We consider fixed-point iterations constructed by simple transforming from a quadratic matrix equation to equivalent fixed-point equations and assume that the iterations are well-defined at some solutions. In that case, we suggest real valued functions. These functions provide radii at the solution, which guarantee the local convergence and the uniqueness of the solutions. Moreover, these radii obtained by simple calculations of some constants. We get the constants by arbitrary matrix norm for coefficient matrices and solution. In numerical experiments, the examples show that the functions give suitable boundaries which guarantee the local convergence and the uniqueness of the solutions for the given equations.