• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.773-781
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• 2010

Recently, Yun [8] proposed a new three-step iterative method with the fourth-order convergence for solving nonlinear equations. By using his ideas, we develop a general form of multi-step iterative methods with higher order convergence for solving nonlinear equations, and then we study convergence analysis of the multi-step iterative methods. Lastly, some numerical experiments are given to illustrate the performance of the multi-step iterative methods.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.219-225
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• 1998

The parameters in linear models with censored normal responses are usually estimated by the iterative maximum likelihood and least square methods. However, the iterative least square method is simple but hardly has theoretical justification, and the iterative maximum likelihood estimating equations are complicatedly derived. In this paper, we justify these methods via Wedderburn (1974)'s quasi-likelihood approach. This provides an explicit justification for the iterative least square method and also directly the iterative maximum likelihood method for estimating the regression coefficients.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.383-392
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• 1998

This paper proposes Generalized Stationary Iterative called GSI method. It is shown that the existing stationary iterative methods are special cases of GSI method. Convergence properties of this method are provided and their numerical experiments for linear systems with symmetric positive definite matrix are also provided.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1409-1418
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• 2010

In this paper, we present a preconditioned iterative method for solving linear systems Ax = b, where A is a Z-matrix. We give some comparison theorems to show that the rate of convergence of the new preconditioned iterative method is faster than the rate of convergence of the previous preconditioned iterative method. Finally, we give one numerical example to show that our results are true.

• Ocean Science Journal
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• v.41 no.4
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• pp.195-199
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• 2006

Comparative study was carried out for an acoustic iterative inverse method to estimate bubble size distributions in water. Conventional bubble sizing methods consider only sound attenuation for sizing. Choi and Yoon [IEEE, 26(1), 125-130 (2001)] reported an acoustic iterative inverse method, which extracts the sound speed component from the measured sound attenuation. It can more accurately estimate the bubble size distributions in water than do the conventional methods. The estimation results of acoustic iterative inverse method were compared with other experimental data. The experimental data show good agreement with the estimation from the acoustic iterative inverse method. This iterative technique can be utilized for bubble sizing in the ocean.

• 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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.13 no.12
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• pp.6028-6042
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• 2019

Since Sparse Nonnegative Matrix Factorization (SNMF) method can control the sparsity of the decomposed matrix, and then it can be adopted to control the sparsity of facial feature extraction and recognition. In order to improve the accuracy of SNMF method for facial feature recognition, new additive iterative rules based on the improved iterative step sizes are proposed to improve the SNMF method, and then the traditional multiplicative iterative rules of SNMF are transformed to additive iterative rules. Meanwhile, to further increase the sparsity of the basis matrix decomposed by the improved SNMF method, a threshold-sparse constraint is adopted to make the basis matrix to a zero-one matrix, which can further improve the accuracy of facial feature recognition. The improved SNMF method based on the additive iterative rules and threshold-sparse constraint is abbreviated as ASNMF, which is adopted to recognize the ORL and CK+ facial datasets, and achieved recognition rate of 96% and 100%, respectively. Meanwhile, from the results of the contrast experiments, it can be found that the recognition rate achieved by the ASNMF method is obviously higher than the basic NMF, traditional SNMF, convex nonnegative matrix factorization (CNMF) and Deep NMF.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1067-1074
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• 2011

In this paper, a preconditioned mixed-type splitting iterative method for solving the linear systems Ax = b is presented, where A is a Z-matrix. Then we also obtain some results to show that the rate of convergence of our method is faster than that of the preconditioned AOR (PAOR) iterative method and preconditioned SOR (PSOR) iterative method. Finally, we give one numerical example to illustrate our results.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.2 no.1
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• pp.38-42
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• 2002

A fast iterative solving method of fuzzy relational equation is proposed. It is derived by eliminating a redundant comparison process in the conventional iterative solving method (Pedrycz, 1983). The proposed method is applied to image reconstruction, and confirmed that the computation time is decreased to 1 / 40 with the compression rate of 0.0625. Furthermore, in order to make any initial solution converge on a reconstructed image with a good quality, a new cost function is proposed. Under the condition that the compression rate is 0.0625, it is confirmed that the root mean square error of the proposed method decreases to 27.34% and 86.27% compared with those of the conventional iterative method and a non iterative image reconstruction method, respectively.

• Journal of electromagnetic engineering and science
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• v.9 no.1
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• pp.12-16
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• 2009

This paper presents a new iterative locally one-dimensional [mite-difference time-domain(LOD-FDTD) method that has a simpler formula than the original iterative LOD-FDTD formula[l]. There are fewer arithmetic operations than in the original LOD-FDTD scheme. This leads to a reduction of CPU time compared to the original LOD-FDTD method while the new method exhibits the same numerical accuracy as the iterative ADI-FDTD scheme. The number of arithmetic operations shows that the efficiency of this method has been improved approximately 20 % over the original iterative LOD-FDTD method.