• Journal of Advanced Navigation Technology
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• v.4 no.1
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• pp.45-49
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• 2000

A GPS measurement solution, in general, is obtained as a least squares solution since the measurement includes errors such as clock errors, ionospheric and tropospheric delays, multipath effect etc. Because of the nonlinearity of the measurement equation, we utilize the nonlinear Newton algorithm to obtain a least squares solution, or mostly, use its linearized algorithm which is more convenient and effective. In this study we developed a fixed point algorithm and proved its availability to replace the nonlinear Newton algorithm and the linearized algorithm. A nonlinear Newton algorithm and a linearized algorithm have the advantage of fast convergence, while their initial values have to be near the unknown solution. On the contrary, the fixed point algorithm provides more reliable but slower convergence even if the initial values are quite far from the solution. Therefore, two types of algorithms may be combined to achieve better performance.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.2782-2784
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• 2001

최대수요전력 제어기의 실시간 부하전력예측을 위하여 Newton 보외법을 적용하였다. 기존의 선형기법에 비하여 실제 데이터에 가까운 부하전력을 예측할 수 있었다. 이 새로운 알고리즘을 적용함으로써 부하예측을 보다 정확히 할 수 있어 빈번한 부하차단이나 우발적인 차단을 방지하여 설비 운용의 신뢰성을 높일 수 있다. 개선된 알고리즘은 마이컴으로 제어되는 실제 시스템에 적용하여 보다 나은 성능을 얻을 수 있었다.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.3
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• pp.294-299
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• 2005

This paper presents the separation performance of the linearly mixed image signals with additive noises by using an independent component analyses(ICAs) of the fixed-point(FP) algorithm based on Newton and secant method, respectively. The Newton's FP-ICA uses the slope of objective function, and the secant's FP-ICA also uses the tangent line of objective function. The 2 kinds of ICA have been applied to the 2 dimensional 2-image with $512\times512$ pixels. Then Gaussian noise and Laplacian noise are added to the mixed images, respectively. The experimental results show that the Newton's FP-ICA has better the separation speed than secant FP-ICA and the secant's FP-ICA has also the better separation rate than Newton's FP-ICA. Especially, the Newton and secant method gives relatively larger improvement degree in separation speed and rate as the noise increases.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.911-923
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• 2016

Machine learning becomes increasingly important in the big data era. Logistic regression is a type of classification in machine leaning, and has been widely used in various fields, including medicine, economics, marketing, and social sciences. Rhipe that integrates R and Hadoop environment, has not been discussed by many researchers owing to the difficulty of its installation and MapReduce implementation. In this paper, we present the MapReduce implementation of Gradient Descent algorithm and Newton-Raphson algorithm for logistic regression using Rhipe. The Newton-Raphson algorithm does not require a learning rate, while Gradient Descent algorithm needs to manually pick a learning rate. We choose the learning rate by performing the mixed procedure of grid search and binary search for processing big data efficiently. In the performance study, our Newton-Raphson algorithm outpeforms Gradient Descent algorithm in all the tested data.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.7B
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• pp.937-943
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• 2001

fast fading 채널 특성을 갖는 DS-CDMA 다중 사용자 환경에서 Normalized CMA(Constant Modulus Algorithm)와 Newton 방식을 이용한 CMA를 이용하여 빠른 수렴속도와 작은 평균 자승 오차(Mean Square Error)를 동시에 개선할 수 있는 등화 방법을 제안하였다. Normalized CMA는 Newton 방식을 이용한 CMA에 비해 작은 평균 자승오차를 갖지만 수렴속도가 느리다는 단점이 있다. 반면 Newton 방식을 이용한 CMA는 Normalized CMA에 비해 수렴속도는 빠르지만 큰 평균 자승 오차를 갖는다는 단점이 있다. 따라서 빠른 수렴 속도와 작은 평균 자승 오차를 동시에 얻기 위한 구조를 제안하였으며, 이 구조는 각각의 알고리즘을 사용하는 방법과는 달리 두 개의 알고리즘을 동시에 이용한다. 모의 실험 결과, 제안한 기법이 Normalized CMA보다 약 320번, Newton 방식을 이용한 CMA보다는 170번 정도 빠른 수렴 속도를 나타냈으며, 동시에 수렴시의 평균 자승 오차는 Newton 방식을 이용한 CMA보다 약 0.6dB, Normalized CMA보다 약 0.4dB 정도 낮은 수치를 나타내는 것을 확인할 수 있었다.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.28 no.11
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• pp.880-885
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• 2017

In AD-MUSIC algorithm, DOD/DOA can be estimated without computationally expensive two-dimensional search. In this paper, to further reduce the computational complexity, the Newton type method has been applied to one-dimensional search. In this paper, we summarize the formulation of the AD-MUSIC algorithm, and present how to apply Newton-type iteration to AD-MUSIC algorithm for improvement of the accuracy of the DOD/DOA estimates. Numerical results are presented to show that the proposed scheme is efficient in the viewpoints of computational burden and estimation accuracy.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.41 no.9
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• pp.1141-1145
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• 2016

In general, a variable forgetting factor is applied to the RLS algorithm for the time-varying parameter estimation in the non-stationary environments. The introduction of a variable forgetting factor to RLS needs heavy additional calculation complexity. We propose a new Gauss Newton variable forgetting factor RLS algorithm which needs small amount of calculation as well as estimates the better parameters in time-varying nonstationary environment. The algorithm performs as good as the conventional Gauss Newton variable forgetting factor RLS and the required additional calculation complexity reduces from $O(N^2)$ to O(N).

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2012.10a
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• pp.47-48
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• 2012

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.223-231
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• 2013

This paper presents a time-domain Gauss-Newton full-waveform inversion method for the material profile reconstruction in heterogeneous semi-infinite solid media. To implement the inverse problem in a finite computational domain, perfectly-matchedlayers( PMLs) are introduced as wave-absorbing boundaries within which the domain's wave velocity profile is to be reconstructed. The inverse problem is formulated in a partial-differential-equations(PDE)-constrained optimization framework, where a least-squares misfit between measured and calculated surface responses is minimized under the constraint of PML-endowed wave equations. A Gauss-Newton-Krylov optimization algorithm is utilized to iteratively update the unknown wave velocity profile with the aid of a specialized regularization scheme. Through a series of one-dimensional examples, the solution of the Gauss-Newton inversion was close enough to the target profile, and showed superior convergence behavior with reduced wall-clock time of implementation compared to a conventional inversion using Fletcher-Reeves optimization algorithm.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.11 no.1
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• pp.46-55
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• 2007

The Newton-Raphson's algorithm for finding a floating point reciprocal and inverse square root calculates the result by performing a fixed number of multiplications. In this paper, an improved Newton-Raphson's algorithm is proposed, that performs multiplications a variable number. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation is derived from many reciprocal and inverse square tables with varying sizes. The superiority of this algorithm is proved by comparing this average number with the fixed number of multiplications of the conventional algorithm. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a reciprocal and inverse square root unit. Also, it can be used to construct optimized approximate tables. The results of this paper can be applied to many areas that utilize floating point numbers, such as digital signal processing, computer graphics, multimedia, scientific computing, etc.