• Title, Summary, Keyword: Moore-Penrose inverse

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A New Approach for Motion Control of Constrained Mechanical Systems: Using Udwadia-Kalaba′s Equations of Motion

  • Joongseon Joh
    • International Journal of Precision Engineering and Manufacturing
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    • v.2 no.4
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    • pp.61-68
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    • 2001
  • A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

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AN ITERATIVE METHOD FOR ORTHOGONAL PROJECTIONS OF GENERALIZED INVERSES

  • Srivastava, Shwetabh;Gupta, D.K.
    • Journal of applied mathematics & informatics
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    • v.32 no.1_2
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    • pp.61-74
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    • 2014
  • This paper describes an iterative method for orthogonal projections $AA^+$ and $A^+A$ of an arbitrary matrix A, where $A^+$ represents the Moore-Penrose inverse. Convergence analysis along with the first and second order error estimates of the method are investigated. Three numerical examples are worked out to show the efficacy of our work. The first example is on a full rank matrix, whereas the other two are on full rank and rank deficient randomly generated matrices. The results obtained by the method are compared with those obtained by another iterative method. The performance measures in terms of mean CPU time (MCT) and the error bounds for computing orthogonal projections are listed in tables. If $Z_k$, k = 0,1,2,... represents the k-th iterate obtained by our method then the sequence of the traces {trace($Z_k$)} is a monotonically increasing sequence converging to the rank of (A). Also, the sequence of traces {trace($I-Z_k$)} is a monotonically decreasing sequence converging to the nullity of $A^*$.

An Analytical Approach for Structural Synthesis of Substructures

  • Eun, Hee-Chang;Park, Sang-Yeol;Lee, Eun-Taik
    • Journal of Mechanical Science and Technology
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    • v.18 no.9
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    • pp.1529-1536
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    • 2004
  • A structure is broken down into a number of substructures by means of the finite element method and the substructures are synthesized for the complete structure. The divided substructures take two types: fixed-free and free-free elements. The flexibility and stiffness matrices of the free-free elements are the Moore-Penrose inverse of each other. Thus, it is not easy to determine the equilibrium equations of the complete structure composed of two mixed types of substructures. This study provides the general form of equilibrium equation of the entire structure through the process of assembling the equilibrium equations of substructures with end conditions of mixed types. Applications demonstrate that the proposed method is effective in the structural analysis of geometrically complicated structures.

COMPLETION OF HANKEL PARTIAL CONTRACTIONS OF NON-EXTREMAL TYPE

  • KIM, IN HYOUN;YOO, SEONGUK;YOON, JASANG
    • Journal of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1003-1021
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    • 2015
  • A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

SINGULAR CASE OF GENERALIZED FIBONACCI AND LUCAS MATRICES

  • Miladinovic, Marko;Stanimirovic, Predrag
    • Journal of the Korean Mathematical Society
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    • v.48 no.1
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    • pp.33-48
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    • 2011
  • The notion of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,s)}$ of type s, whose nonzero elements are generalized Fibonacci numbers, is introduced in the paper [23]. Regular case s = 0 is investigated in [23]. In the present article we consider singular case s = -1. Pseudoinverse of the generalized Fibonacci matrix $\mathcal{F}_n^{(a,b,-1)}$ is derived. Correlations between the matrix $\mathcal{F}_n^{(a,b,-1)}$ and the Pascal matrices are considered. Some combinatorial identities involving generalized Fibonacci numbers are derived. A class of test matrices for computing the Moore-Penrose inverse is presented in the last section.

Image Reconstruction of Eigenvalue of Diffusion Principal Axis Using Diffusion Tensor Imaging (확산텐서영상을 이용한 확산 주축의 고유치 영상 재구성)

  • Kim, In-Seong;Kim, Joo-Hyun;Yeon, Gun;Suh, Kyung-Jin;Yoo, Don-Sik;Kang, Duk-Sik;Bae, Sung-Jin;Chang, Yong-Min
    • Investigative Magnetic Resonance Imaging
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    • v.11 no.2
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    • pp.110-118
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    • 2007
  • Purpose: The objective of this work to construct eigenvalue maps that have information of magnitude of three primary diffusion directions using diffusion tensor images. Materials and Methods: To construct eigenvalue maps, we used a 3.0T MRI scanner. We also compared the Moore-Penrose pseudo-inverse matrix method and the SVD (single value decomposition) method to calculate magnitude of three primary diffusion directions. Eigenvalue maps were constructed by calculating of magnitude of three primary diffusion directions. We did investigate the relationship between eigenvalue maps and fractional anisotropy map. Results: Using Diffusion Tensor Images by diffusion tensor imaging sequence, we did construct eigenvalue maps of three primary diffusion directions. Comparison between eigenvalue maps and Fractional Anisotropy map shows what is difference of Fractional Anisotropy value in brain anatomy. Furthermore, through the simulation of variable eigenvalues, we confirmed changes of Fractional Anisotropy values by variable eigenvalues. And Fractional anisotropy was not determined by magnitude of each primary diffusion direction, but it was determined by combination of each primary diffusion direction. Conclusion: By construction of eigenvalue maps, we can confirm what is the reason of fractional anisotropy variation by measurement the magnitude of three primary diffusion directions on lesion of brain white matter, using eigenvalue maps and fractional anisotropy map.

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The Development and Application of Office Price Index for Benchmark in Seoul using Repeat Sales Model (반복매매모형을 활용한 서울시 오피스 벤치마크 가격지수 개발 및 시험적 적용 연구)

  • Ryu, Kang Min;Song, Ki Wook
    • LHI Journal of Land, Housing, and Urban Affairs
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    • v.11 no.2
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    • pp.33-46
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    • 2020
  • As the fastest growing office transaction volume in Korea, there's been a need for development of indicators to accurately diagnose the office capital market. The purpose of this paper is experimentally calculate to the office price index for effective benchmark indices in Seoul. The quantitative methodology used a Case-Shiller Repeat Sales Model (1991), based on actual multiple office transaction dataset with over minimum 1,653 ㎡ from Q3 1999 to 4Q 2019 in the case of 1,536 buildings within Seoul Metropolitan. In addition, the collected historical data and spatial statistical analysis tools were treated with the SAS 9.4 and ArcGIS 10.7 programs. The main empirical results of research are briefly summarized as follows; First, Seoul office price index was estimated to be 344.3 point (2001.1Q=100.0P) at the end of 2019, and has more than tripled over the past two decades. it means that the sales price of office per 3.3 ㎡ has consistently risen more than 12% every year since 2000, which is far above the indices for apartment housing index, announced by the MOLIT (2009). Second, between quarterly and annual office price index for the two-step estimation of the MIT Real Estate Research Center (MIT/CRE), T, L, AL variables have statistically significant coefficient (Beta) all of the mode l (p<0.01). Third, it was possible to produce a more stable office price index against the basic index by using the Moore-Penrose's pseoudo inverse technique at low transaction frequency. Fourth, as an lagging indicators, the office price index is closely related to key macroeconomic indicators, such as GDP(+), KOSPI(+), interest rates (5-year KTB, -). This facts indicate that long-term office investment tends to outperform other financial assets owing to high return and low risk pattern. In conclusion, these findings are practically meaningful to presenting an new office price index that increases accuracy and then attempting to preliminary applications for the case of Seoul. Moreover, it can provide sincerely useful benchmark about investing an office and predicting changes of the sales price among market participants (e.g. policy maker, investor, landlord, tenant, user) in the future.