• Title/Summary/Keyword: Sparse linear system

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Parallel solution of linear systems on the CRAY-2 using multi/micro tasking library (CRAY-2에서 멀티/마이크로 태스킹 라이브러리를 이용한 선형시스템의 병렬해법)

  • Ma, Sang-Back
    • The Transactions of the Korea Information Processing Society
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    • v.4 no.11
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    • pp.2711-2720
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    • 1997
  • Multitasking and microtasking on the CRAY machine provides still another way to improve computational power. Since CRAY-2 has 4 processors we can achieve speedup up to 4 properly designed algorithms. In this paper we present two parallelizations of linear system solution in the CRAY-2 with multitasking and microtasking library. One is the LU decomposition on the dense matrices and the other is the iterative solution of large sparse linear systems with the preconditioner proposed by Radicati di Brozolo. In the first case we realized a speedup of 1.3 with 2 processors for a matrix of dimension 600 with the multitasking and in the second case a speedup of around 3 with 4 processors for a matrix of dimension 600 with the multitasking and in the second case a speedup of around 3 with 4 processors for a matrix of dimension 8192 with the microtasking. In the first case the speedup is limited because of the nonuniform vector lenghts. In the second case the ILU(0) preconditioner with Radicati's technique seem to realize a reasonable high speedup with 4 processors.

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Why Gabor Frames? Two Fundamental Measures of Coherence and Their Role in Model Selection

  • Bajwa, Waheed U.;Calderbank, Robert;Jafarpour, Sina
    • Journal of Communications and Networks
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    • v.12 no.4
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    • pp.289-307
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    • 2010
  • The problem of model selection arises in a number of contexts, such as subset selection in linear regression, estimation of structures in graphical models, and signal denoising. This paper studies non-asymptotic model selection for the general case of arbitrary (random or deterministic) design matrices and arbitrary nonzero entries of the signal. In this regard, it generalizes the notion of incoherence in the existing literature on model selection and introduces two fundamental measures of coherence-termed as the worst-case coherence and the average coherence-among the columns of a design matrix. It utilizes these two measures of coherence to provide an in-depth analysis of a simple, model-order agnostic one-step thresholding (OST) algorithm for model selection and proves that OST is feasible for exact as well as partial model selection as long as the design matrix obeys an easily verifiable property, which is termed as the coherence property. One of the key insights offered by the ensuing analysis in this regard is that OST can successfully carry out model selection even when methods based on convex optimization such as the lasso fail due to the rank deficiency of the submatrices of the design matrix. In addition, the paper establishes that if the design matrix has reasonably small worst-case and average coherence then OST performs near-optimally when either (i) the energy of any nonzero entry of the signal is close to the average signal energy per nonzero entry or (ii) the signal-to-noise ratio in the measurement system is not too high. Finally, two other key contributions of the paper are that (i) it provides bounds on the average coherence of Gaussian matrices and Gabor frames, and (ii) it extends the results on model selection using OST to low-complexity, model-order agnostic recovery of sparse signals with arbitrary nonzero entries. In particular, this part of the analysis in the paper implies that an Alltop Gabor frame together with OST can successfully carry out model selection and recovery of sparse signals irrespective of the phases of the nonzero entries even if the number of nonzero entries scales almost linearly with the number of rows of the Alltop Gabor frame.

Performance of direction-of-arrival estimation of SpSF in frequency domain: in case of non-uniform sensor array (주파수 영역으로 구현한 SpSF알고리듬: 비균일 센서 환경에서의 도래각 추정 성능)

  • Paik, Ji Woong;Zhang, Xueyang;Hong, Wooyoung;Hong, Jungpyo;Kim, Seongil;Lee, Joon-Ho
    • The Journal of the Acoustical Society of Korea
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    • v.39 no.3
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    • pp.191-199
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    • 2020
  • Currently, studies on the estimation algorithm based on compressive sensing are actively underway, but to the best of our knowledge, no study on the performance of the Sparse Spectrum Fitting (SpSF) algorithm in nonuniform sensor arrays has been made. This paper deals with the derivation of the compressive sensing based covariance fitting algorithm extended to the frequency domain. In addition, it shows the performance of directon-of-arrival estimation of the frequency domain SpSF algorithm in non-uniform linear sensor array system and the sensor array failure situation.

Effect of PE Film Mulching and Planting Density on Growth and Tuber Yield in Yacon(Polymina sonchifolia POEPP) (재식밀도와 비닐피복이 야콘의 생육 및 수량에 미치는 영향)

  • 신동영;이영만;김학진
    • KOREAN JOURNAL OF CROP SCIENCE
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    • v.38 no.3
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    • pp.240-244
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    • 1993
  • Yacon(Polymina sonchifolia POEPP), an indigenous Andean natural resource food plant, was imported as a new root crop from New Zealand in 1986. However the chemical composition and planting system of it have not been research in Korea. The experimental results for the optimum planting densities and mulching effect are as follows. Height of the main stem of yacon was grown linear from July to October, is showed more fast growth as density increased, and showed highest in 70 ${\times}$ 55cm density. The tiller was bubed 3 month after planting but there was no significant difference among mulching, non-mulching condition and planting density. The fresh weight of root of mulching condition was heavier than that in non-mulching condition and 70 ${\times}$ 40cm mulching condition. In mulching treatment, number of roots in dense planting were more than that in sparse planting. The effect of mulching was not shown significantly in root diameter and root length.

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Stereo Semi-direct Visual Odometry with Adaptive Motion Prior Weights of Lunar Exploration Rover (달 탐사 로버의 적응형 움직임 가중치에 따른 스테레오 준직접방식 비주얼 오도메트리)

  • Jung, Jae Hyung;Heo, Se Jong;Park, Chan Gook
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.46 no.6
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    • pp.479-486
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    • 2018
  • In order to ensure reliable navigation performance of a lunar exploration rover, navigation algorithms using additional sensors such as inertial measurement units and cameras are essential on lunar surface in the absence of a global navigation satellite system. Unprecedentedly, Visual Odometry (VO) using a stereo camera has been successfully implemented at the US Mars rovers. In this paper, we estimate the 6-DOF pose of the lunar exploration rover from gray images of a lunar-like terrains. The proposed algorithm estimates relative pose of consecutive images by sparse image alignment based semi-direct VO. In order to overcome vulnerability to non-linearity of direct VO, we add adaptive motion prior weights calculated from a linear function of the previous pose to the optimization cost function. The proposed algorithm is verified in lunar-like terrain dataset recorded by Toronto University reflecting the characteristics of the actual lunar environment.

3D Modeling and Inversion of Magnetic Anomalies (자력이상 3차원 모델링 및 역산)

  • Cho, In-Ky;Kang, Hye-Jin;Lee, Keun-Soo;Ko, Kwang-Beom;Kim, Jong-Nam;You, Young-June;Han, Kyeong-Soo;Shin, Hong-Jun
    • Geophysics and Geophysical Exploration
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    • v.16 no.3
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    • pp.119-130
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    • 2013
  • We developed a method for inverting magnetic data to recover the 3D susceptibility models. The major difficulty in the inversion of the potential data is the non-uniqueness and the vast computing time. The insufficient number of data compared with that of inversion blocks intensifies the non-uniqueness problem. Furthermore, there is poor depth resolution inherent in magnetic data. To overcome this non-uniqueness problem, we propose a resolution model constraint that imposes large penalty on the model parameter with good resolution; on the other hand, small penalty on the model parameter with poor resolution. Using this model constraint, the model parameter with a poor resolution can be effectively resolved. Moreover, the wavelet transform and parallel solving were introduced to save the computing time. Through the wavelet transform, a large system matrix was transformed to a sparse matrix and solved by a parallel linear equation solver. This procedure is able to enormously save the computing time for the 3D inversion of magnetic data. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and real airborne data obtained at the Geumsan area of Korea.