• Title, Summary, Keyword: Moore-Penrose inverse

### A Study on the Shape Analysis Method of Plane Truss Structures under the Prescribed Displacement (변위제약을 받는 평면트러스 구조물의 형태해석기법에 관한 연구)

• 문창훈;한상을
• Computational Structural Engineering
• /
• v.11 no.1
• /
• pp.217-226
• /
• 1998
• The purpose of this study is to develop a technique for the shape analysis of plane truss structures under prescribed displacement modes. The shape analysis is performed based on the existence theorem of the solution and the Moore-Penrose generalized inverse matrix. In this paper, the homologous deformation of structures was proposed as prescribed displacement modes, the shape of the structure is determined from these various modes and applied loads. In general, the shape analysis is a kind of inverse problem different from stress analysis, and the governing equation becomes nonlinear. In this regard, Newton-Raphson method was used to solve the nonlinear equation. Three different shape models are investigated as numerical examples to show the accuracy and the effectiveness of the proposed method.

### HIGHER ORDER ITERATIONS FOR MOORE-PENROSE INVERSES

• Srivastava, Shwetabh;Gupta, D.K.
• Journal of applied mathematics & informatics
• /
• v.32 no.1_2
• /
• pp.171-184
• /
• 2014
• A higher order iterative method to compute the Moore-Penrose inverses of arbitrary matrices using only the Penrose equation (ii) is developed by extending the iterative method described in [1]. Convergence properties as well as the error estimates of the method are studied. The efficacy of the method is demonstrated by working out four numerical examples, two involving a full rank matrix and an ill-conditioned Hilbert matrix, whereas, the other two involving randomly generated full rank and rank deficient matrices. The performance measures are the number of iterations and CPU time in seconds used by the method. It is observed that the number of iterations always decreases as expected and the CPU time first decreases gradually and then increases with the increase of the order of the method for all examples considered.

### A DFT Deblurring Algorithm of Blind Blur Image (무정보 blur 이미지 복구를 위한 DFT 변환)

• Moon, Kyung-Il;Kim, Chul
• Journal of The Korean Association of Information Education
• /
• v.15 no.3
• /
• pp.517-524
• /
• 2011
• This paper presents a fast blind deconvolution method that produces a deblurring result from a single image in only a few seconds. The high speed of our method is enabled by considering the Discrete Fourier Transform (DFT), and its relation to filtering and convolution, and fast computation of Moore-Penrose inverse matrix. How can we predict the behavior of an arbitrary filter, or even more to the point design a filter to achieve certain specifications. The idea is to study the frequency response of the filter. This concept leads to an useful convolution formula. A Matlab implementation of our method usually takes less than one minute to deblur an image of moderate size, while the deblurring quality is comparable.

### Parameter Optimization of Extreme Learning Machine Using Bacterial Foraging Algorithm (Bacterial Foraging Algorithm을 이용한 Extreme Learning Machine의 파라미터 최적화)

• Cho, Jae-Hoon;Lee, Dae-Jong;Chun, Myung-Geun
• Journal of the Korean Institute of Intelligent Systems
• /
• v.17 no.6
• /
• pp.807-812
• /
• 2007
• Recently, Extreme learning machine(ELM), a novel learning algorithm which is much faster than conventional gradient-based learning algorithm, was proposed for single-hidden-layer feedforward neural networks. The initial input weights and hidden biases of ELM are usually randomly chosen, and the output weights are analytically determined by using Moore-Penrose(MP) generalized inverse. But it has the difficulties to choose initial input weights and hidden biases. In this paper, an advanced method using the bacterial foraging algorithm to adjust the input weights and hidden biases is proposed. Experiment at results show that this method can achieve better performance for problems having higher dimension than others.

### SINGULAR INTEGRAL EQUATIONS AND UNDERDETERMINED SYSTEMS

• KIM, SEKI
• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.67-80
• /
• 1998
• In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

### Dynamic analysis of deployable structures using independent displacement modes based on Moore-Penrose generalized inverse matrix

• Xiang, Ping;Wu, Minger;Zhou, Rui Q.
• Structural Engineering and Mechanics
• /
• v.54 no.6
• /
• pp.1153-1174
• /
• 2015
• Deployable structures have gained more and more applications in space and civil structures, while it takes a large amount of computational resources to analyze this kind of multibody systems using common analysis methods. This paper presents a new approach for dynamic analysis of multibody systems consisting of both rigid bars and arbitrarily shaped rigid bodies. The bars and rigid bodies are connected through their nodes by ideal pin joints, which are usually fundamental components of deployable structures. Utilizing the Moore-Penrose generalized inverse matrix, equations of motion and constraint equations of the bars and rigid bodies are formulated with nodal Cartesian coordinates as unknowns. Based on the constraint equations, the nodal displacements are expressed as linear combination of the independent modes of the rigid body displacements, i.e., the null space orthogonal basis of the constraint matrix. The proposed method has less unknowns and a simple formulation compared with common multibody dynamic methods. An analysis program for the proposed method is developed, and its validity and efficiency are investigated by analyses of several representative numerical examples, where good accuracy and efficiency are demonstrated through comparison with commercial software package ADAMS.

### Motion Control Design of Constrained Mechanical Systems (구속된 기계시스템의 운동제어 설계)

• 조중선
• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.7
• /
• pp.154-162
• /
• 1997
• 본 논문은 구속된 기계 시스템의 운동 제어 설계를 위한 새로운 방법을 제안한다. 구속된 기계 시스템의 운동 제어에는 지금까지 주로 사용되어온 Lagrange의 운동 방정식에 의한 모델링 보다 Udwadia와 Kalaba에 의해 제안된 운동 방정식에 의한 모델링이 더욱 적합함을 보였으며 이는 Holonomic 및 Nonholonomic 구속 조건을 비롯한 대부분의 구속 조건이 포함된다. 문헌에 잘 알려진 두 시스템을 시뮬레이션을 통하여 비교 함으로써 본 논문에 제안된 방법이 보다 우수한 결과를 보여줌을 확인 할 수 있었다. 또한 지금까지 불가능 하였던 비선형 일반 속도(gereralized velocity)를 포함한 구속 조건도 용이하게 제어됨을 보임으로써 광범위한 구속된 기계 시스템의 제어 문제를 통일된 방법으로 접근 할 수 있음을 제시하였다.

### A Study on Numerical Analysis of Equation of Motion for Constrained Systems (구속된 시스템 운동방정식의 수치해석에 관한 연구)

• 은희창;정헌수
• Journal of KSNVE
• /
• v.7 no.5
• /
• pp.773-780
• /
• 1997
• Using Generalized Inverse Method presented by Udwadia and Kalaba in 1992, we can obtain equations to exactly describe the motion of constrained systems. When the differential equations are numerically integrated by any numerical integration scheme, the numerical results are generally found to veer away from satisfying constraint equations. Thus, this paper deals with the numerical integration of the differential equations describing constrained systems. Based on Baumgarte method, we propose numerical methods for reducing the errors in the satisfaction of the constraints.

### SEMI-CONVERGENCE OF THE PARAMETERIZED INEXACT UZAWA METHOD FOR SINGULAR SADDLE POINT PROBLEMS

• YUN, JAE HEON
• Bulletin of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1669-1681
• /
• 2015
• In this paper, we provide semi-convergence results of the parameterized inexact Uzawa method with singular preconditioners for solving singular saddle point problems. We also provide numerical experiments to examine the effectiveness of the parameterized inexact Uzawa method with singular preconditioners.

### Whole learning algorithm of the neural network for modeling nonlinear and dynamic behavior of RC members

• Satoh, Kayo;Yoshikawa, Nobuhiro;Nakano, Yoshiaki;Yang, Won-Jik
• Structural Engineering and Mechanics
• /
• v.12 no.5
• /
• pp.527-540
• /
• 2001
• A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.