• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
• /
• pp.91-94
• /
• 1996

This paper presents an approach to estimation of learning gain in iterative learning control for discrete-time affine nonlinear systems. In iterative learning control, to determine learning gain satisfying the convergence condition, we have to know the system model. In the proposed method, the input-output equation of a system is identified by neural network refered to as Piecewise Linearly Trained Network (PLTN). Then from the input-output equation, the learning gain in iterative learning law is estimated. The validity of our method is demonstrated by simulations.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제9권4호
• /
• pp.390-403
• /
• 2017

Smoothed Particle Hydrodynamics (SPH) method has a good adaptability for the simulation of free surface flow problems. There are two forms of SPH. One is weak compressible SPH and the other one is incompressible SPH (ISPH). Compared with the former one, ISPH method performs better in many cases. ISPH based on Rankine source solution can perform better than traditional ISPH, as it can use larger stepping length by avoiding the second order derivative in pressure Poisson equation. However, ISPH_R method needs to solve the sparse linear matrix for pressure Poisson equation, which is one of the most expensive parts during one time stepping calculation. Iterative methods are normally used for solving Poisson equation with large particle numbers. However, there are many iterative methods available and the question for using which one is still open. In this paper, three iterative methods, CGS, Bi-CGstab and GMRES are compared, which are suitable and typical for large unsymmetrical sparse matrix solutions. According to the numerical tests on different cases, still water test, dam breaking, violent tank sloshing, solitary wave slamming, the GMRES method is more efficient than CGS and Bi-CGstab for ISPH method.

• 대한수학회논문집
• /
• 제9권4호
• /
• pp.819-823
• /
• 1994

If H is a Hilbert space, then an operator $T : D(T) \subset H \to H$ is said to be monotone if $$ (x-y, Tx-Ty) \geq 0$$ for any x, y in D(T). Many authors [1], [4] obtained the existence theorem for the equation $y = x + Tx$ for x, given an element y in H and a monotone operator T. On the other hand some iterative methods were applied to the approximations for the solution of the above equation [6], [8]. For example Bruck [2] obtained the iterative solution of the above equation with an explicit error estimate as follows.

• 대한수학회논문집
• /
• 제20권1호
• /
• pp.71-78
• /
• 2005

In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$-strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].

• 대한수학회논문집
• /
• 제19권3호
• /
• pp.461-467
• /
• 2004

In this paper, we study the Ishikawa iterative sequences with errors for Lipschitzian strongly pseudo-contractive operator in arbitrary real Banach spaces. Our results improve the results obtained previously by C. E. Chidume [3] and Zeng [9].

• Journal of applied mathematics & informatics
• /
• 제27권5_6호
• /
• pp.1061-1071
• /
• 2009

For real generalized reflexive matrices R, S, i.e., $R^T$ = R, $R^2$ = I, $S^T$ = S, $S^2$ = I, we say that real matrix X is (R,S)-symmetric, if RXS = X. In this paper, an iterative algorithm is proposed to solve the least-squares problem of matrix equation AXB = C with (R,S)-symmetric X. Furthermore, the optimal approximation solution to given matrix $X_0$ is also derived by this iterative algorithm. Finally, given numerical example and its convergent curve show that this method is feasible and efficient.

• Nonlinear Functional Analysis and Applications
• /
• 제29권1호
• /
• pp.179-195
• /
• 2024

In this article, we study the Picard-Ishikawa iterative method for approximating the fixed point of generalized α-Reich-Suzuki nonexpanisive mappings. The weak and strong convergence theorems of the considered method are established with mild assumptions. Numerical example is provided to illustrate the computational efficiency of the studied method. We apply our results to the solution of a nonlinear delay integral equation. The results in this article are improvements of well-known results.

• Current Optics and Photonics
• /
• 제5권3호
• /
• pp.322-328
• /
• 2021

In this paper, a pretreatment method for a matrix in convex optimization is proposed to optimize the spectral reconstruction process of a disordered dispersion spectrometer. Unlike the reconstruction process of traditional spectrometers using Fourier transforms, the reconstruction process of disordered dispersion spectrometers involves solving a large-scale matrix equation. However, since the matrices in the matrix equation are obtained through measurement, they contain uncertainties due to out of band signals, background noise, rounding errors, temperature variations and so on. It is difficult to solve such a matrix equation by using ordinary nonstationary iterative methods, owing to instability problems. Although the smoothing Tikhonov regularization approach has the ability to approximatively solve the matrix equation and reconstruct most simple spectral shapes, it still suffers the limitations of reconstructing complex and irregular spectral shapes that are commonly used to distinguish different elements of detected targets with mixed substances by characteristic spectral peaks. Therefore, we propose a special pretreatment method for a matrix in convex optimization, which has been proved to be useful for reducing the condition number of matrices in the equation. In comparison with the reconstructed spectra gotten by the previous ordinary iterative method, the spectra obtained by the pretreatment method show obvious accuracy.

• 한국정보과학회논문지:소프트웨어및응용
• /
• 제32권8호
• /
• pp.795-807
• /
• 2005

기존의 LVA를 수행하는 알고리즘은 반복적 정보흐름분석(Iterative Data Flow Analysis -DFA) 프레임워크에 따라 프로그램 전체를 반복적으로 스캔하면서 진행되어진다. Zephyr[1] 컴파일러의 경우 이와 같은 반복적 알고리즘으로 LVA를 수행하는 시간이 전체 컴파일 시간에서 약 $7\%$를 차지하고 있다. 기존 LVA 알고리즘은 여러 가지로 개선할 점들이 있다. LVA를 수행하는 기존의 반복적 알고리즘은 알고리즘의 특성상 방문하지 않아도 되는 basic block들에 대한 방문이 잦고, 살아있는 변수들의 집합을 점차적으로 증가해 가면서 구하는 특성상 큰 변수들의 집합에 대한 연산을 계속 하게 된다. 우리는 기존의 알고리즘과 달리 사용된 변수들(USE set)에 대해 Control Flow Graph(CFG)에서 거슬러 올라가면서 LVA를 수행하는 반복적인 알고리즘의 개선안을 제안하고자 한다. 이는 기존의 알고리즘과 같은 결과를 내면서 더 빠른 알고리즘이다. DFA에서의 flow equation을 적용하는 순서를 바꿈으로써 많은 중복 계산을 줄일 수 있다. 이러한 방법으로 인해 basic block을 방문해야만 하는 횟수를 줄이면서 전체 수행 시간을 단축시킨다. 간단한 추가 구현만으로 Zephyr 컴파일러에서의 실험 결과에서 LVA만을 수행하는 시간에서 기존의 알고리즘보다 $36.4\%$ 짧은 시간을 사용하였고, 이는 전체 컴파일 시간을 $2.6\%$ 줄이는 효과를 가져왔다.

• Journal of applied mathematics & informatics
• /
• 제27권1_2호
• /
• pp.1-12
• /
• 2009

Iterative algorithms are proposed for the least-squares symmetric solution of AXB = E with a submatrix constraint. We characterize the linear mappings from their independent element space to the constrained solution sets, study their properties and use these properties to propose two matrix iterative algorithms that can find the minimum and quasi-minimum norm solution based on the classical LSQR algorithm for solving the unconstrained LS problem. Numerical results are provided that show the efficiency of the proposed methods.