• 제목/요약/키워드: least-squares problem

검색결과 347건 처리시간 0.029초

Improved Element-Free Galerkin method (IEFG) for solving three-dimensional elasticity problems

  • Zhang, Zan;Liew, K.M.
    • Interaction and multiscale mechanics
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    • 제3권2호
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    • pp.123-143
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    • 2010
  • The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

A PRECONDITIONER FOR THE LSQR ALGORITHM

  • Karimi, Saeed;Salkuyeh, Davod Khojasteh;Toutounian, Faezeh
    • Journal of applied mathematics & informatics
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    • 제26권1_2호
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    • pp.213-222
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    • 2008
  • Iterative methods are often suitable for solving least squares problems min$||Ax-b||_2$, where A $\epsilon\;\mathbb{R}^{m{\times}n}$ is large and sparse. The well known LSQR algorithm is among the iterative methods for solving these problems. A good preconditioner is often needed to speedup the LSQR convergence. In this paper we present the numerical experiments of applying a well known preconditioner for the LSQR algorithm. The preconditioner is based on the $A^T$ A-orthogonalization process which furnishes an incomplete upper-lower factorization of the inverse of the normal matrix $A^T$ A. The main advantage of this preconditioner is that we apply only one of the factors as a right preconditioner for the LSQR algorithm applied to the least squares problem min$||Ax-b||_2$. The preconditioner needs only the sparse matrix-vector product operations and significantly reduces the solution time compared to the unpreconditioned iteration. Finally, some numerical experiments on test matrices from Harwell-Boeing collection are presented to show the robustness and efficiency of this preconditioner.

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Active damage localization technique based on energy propagation of Lamb waves

  • Wang, Lei;Yuan, F.G.
    • Smart Structures and Systems
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    • 제3권2호
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    • pp.201-217
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    • 2007
  • An active damage detection technique is introduced to locate damage in an isotropic plate using Lamb waves. This technique uses a time-domain energy model of Lamb waves in plates that the wave amplitude inversely decays with the propagation distance along a ray direction. Accordingly the damage localization is formulated as a least-squares problem to minimize an error function between the model and the measured data. An active sensing system with integrated actuators/sensors is controlled to excite/receive $A_0$ mode of Lamb waves in the plate. Scattered wave signals from the damage can be obtained by subtracting the baseline signal of the undamaged plate from the recorded signal of the damaged plate. In the experimental study, after collecting the scattered wave signals, a discrete wavelet transform (DWT) is employed to extract the first scattered wave pack from the damage, then an iterative method is derived to solve the least-squares problem for locating the damage. Since this method does not rely on time-of-flight but wave energy measurement, it is more robust, reliable, and noise-tolerant. Both numerical and experimental examples are performed to verify the efficiency and accuracy of the method, and the results demonstrate that the estimated damage position stably converges to the targeted damage.

1차원 자유경계문제의 해석을 위한 Implicit 이동최소제곱 차분법 (Implicit Moving Least Squares Difference Method for 1-D Moving Boundary Problem)

  • 윤영철
    • 한국전산구조공학회논문집
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    • 제25권5호
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    • pp.439-446
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    • 2012
  • 본 논문은 1차원 자유경계문제 해석의 정확도 향상을 위해 이동최소제곱 차분법을 이용하여 이동경계의 위상변화를 implicit하게 추적하는 기법을 제시한다. 기존의 이동최소제곱 차분법은 이동경계의 위치를 explicit하게 진전시켜 반복계산은 필요없지만 해의 정확도 감소를 피할 수 없었다. 그러나 본 연구에서 제시한 implicit 기법은 전체 계방정식이 비선형 시스템이 되어 반복계산 과정이 필요하지만, 실제로 수치예제를 통해 검증해 본 결과 계산량의 큰 증가없이 해석의 정확도를 획기적으로 향상시켰다. 이동하는 미분불연속 특이성을 갖는 융해(melting)문제를 수치계산한 결과, implicit 이동최소제곱 차분법을 통해 2차정확도를 얻을 수 있음을 보였다.

Support vector expectile regression using IRWLS procedure

  • Choi, Kook-Lyeol;Shim, Jooyong;Seok, Kyungha
    • Journal of the Korean Data and Information Science Society
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    • 제25권4호
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    • pp.931-939
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    • 2014
  • In this paper we propose the iteratively reweighted least squares procedure to solve the quadratic programming problem of support vector expectile regression with an asymmetrically weighted squares loss function. The proposed procedure enables us to select the appropriate hyperparameters easily by using the generalized cross validation function. Through numerical studies on the artificial and the real data sets we show the effectiveness of the proposed method on the estimation performances.

A New TLS-Based Sequential Algorithm to Identify Two Failed Satellites

  • Jeon Chang-Wan;Lachapelle Gerard
    • International Journal of Control, Automation, and Systems
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    • 제3권2호
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    • pp.166-172
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    • 2005
  • With the development of RAIM techniques for single failure, increasing interest has been shown in the multiple failure problem. As a result, numerous approaches have been used in attempts to tackle this problem. This paper considers the two failure problem with total least squares (TLS) technique, a solution that has rarely been addressed because TLS requires an immense number of computations. In this paper, the special form of the observation matrix H, (that is, one column is exactly known) is exploited so as to develop an algorithm in a sequential form, thereby reducing computational load. The algorithm permits the advantages of TLS without the excessive computational burden. The proposed algorithm is verified through a numerical simulation.

비용함수와 서브 골을 이용한 비선형 최적화 방법 기반의 이동로봇 장애물 회피 주행 (Mobile Robot Navigation with Obstacle Avoidance based on the Nonlinear Least Squares Optimization Method using the Cost Function and the Sub-Goal Switching)

  • 정영종;김곤우
    • 전기학회논문지
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    • 제63권9호
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    • pp.1266-1272
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    • 2014
  • We define the mobile robot navigation problem as an optimization problem to minimize the cost function with the pose error between the goal position and the position of a mobile robot. Using Gauss-Newton method for the optimization, the optimal speeds of the left and right wheels can be found as the solution of the optimization problem. Especially, the rotational speed of wheels of a mobile robot can be directly related to the overall speed of a mobile robot using the Jacobian derived from the kinematic model. When the robot detects the obstacle using sensors, the sub-goal switching method is adopted for the efficient obstacle avoidance during the navigation. The performance was evaluated using the simulation and the simulation results show the validity of the proposed method.

Extension and Appication of Total Least Squares Method for the Identification of Bilinear Systems

  • Han, Seok-Won;Kim, Jin-Young;Sung, Koeng-Mo
    • The Journal of the Acoustical Society of Korea
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    • 제15권1E호
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    • pp.59-64
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    • 1996
  • When the input-output record is available, the identification of a bilinear system is considered. It is assumed that the input is noise free and the output is contaminated by an additive noise. It is further assumed that the covariance matrix of the noise is known up to a factor of proportionality. The extended generalized total least squares (e-GTLS) method is proposed as one of the consistent estimators of the bilinear system parameters. Considering that the input is noise-free and that bilinear system equation is linear with respect to the system parameters, we extend the GTLS problem. The extended GTLS problem is reduced to an unconstrained minimization problem, and is solved by the Newton-Raphson method. We compare the GTLS method and the e-GTLS method in the point of the accuracy of the estimated system parameters.

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Simple factor analysis of measured data

  • Kozar, Ivica;Kozar, Danila Lozzi;Malic, Neira Toric
    • Coupled systems mechanics
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    • 제11권1호
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    • pp.33-41
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    • 2022
  • Quite often we have a lot of measurement data and would like to find some relation between them. One common task is to see whether some measured data or a curve of known shape fit into the cumulative measured data. The problem can be visualized since data could generally be presented as curves or planes in Cartesian coordinates where each curve could be represented as a vector. In most cases we have measured the cumulative 'curve', we know shapes of other 'curves' and would like to determine unknown coefficients that multiply the known shapes in order to match the measured cumulative 'curve'. This problem could be presented in more complex variants, e.g., a constant could be added, some missing (unknown) data vector could be added to the measured summary vector, and instead of constant factors we could have polynomials, etc. All of them could be solved with slightly extended version of the procedure presented in the sequel. Solution procedure could be devised by reformulating the problem as a measurement problem and applying the generalized inverse of the measurement matrix. Measurement problem often has some errors involved in the measurement data but the least squares method that is comprised in the formulation quite successfully addresses the problem. Numerical examples illustrate the solution procedure.