• Title/Summary/Keyword: Jacobi Algorithm

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FPGA Implementation of Unitary MUSIC Algorithm for DoA Estimation (도래방향 추정을 위한 유니터리 MUSIC 알고리즘의 FPGA 구현)

  • Ju, Woo-Yong;Lee, Kyoung-Sun;Jeong, Bong-Sik
    • Journal of the Institute of Convergence Signal Processing
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    • v.11 no.1
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    • pp.41-46
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    • 2010
  • In this paper, the DoA(Direction of Arrival) estimator using unitary MUSIC algorithm is studied. The complex-valued correlation matrix of MUSIC algorithm is transformed to the real-valued one using unitary transform for easy implementation. The eigenvalue and eigenvector are obtained by the combined Jacobi-CORDIC algorithm. CORDIC algorithm can be implemented by only ADD and SHIFT operations and MUSIC spectrum computed by 256 point DFT algorithm. Results of unitary MUSIC algorithm designed by System Generator for FPGA implementation is entirely consistent with Matlab results. Its performance is evaluated through hardware co-simulation and resource estimation.

A CORDIC-Jacobi Based Spectrum Sensing Algorithm For Cognitive Radio

  • Tan, Xiaobo;Zhang, Hang
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.6 no.9
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    • pp.1998-2016
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    • 2012
  • Reliable spectrum sensing algorithm is a fundamental component in cognitive radio. In this paper, a non-cooperative spectrum sensing algorithm which needs only one cognitive radio node named CORDIC (Coordinate Rotation Digital Computer) Jacobi based method is proposed. The algorithm computes the eigenvalues of the sampled covariance of received signal mainly by shift and additional operations, which is suitable for hardware implementation. Based the latest random matrix theory (RMT) about the distribution of the limiting maximum and minimum eigenvalue ratio, the relationship between the probability of false alarm and the decision threshold is derived. Simulations and discussions show the method is effective. Real captured digital television (DTV) signals and Universal Software Radio Peripheral (USRP) are also employed to evaluate the performance of the algorithm, which prove the proposed algorithm can be applied in practical spectrum sensing applications.

An Efficient Parallel Algorithm for Solving Large Sparse Linear Systems of Equations (대형 Sparse 선형시스템 방정식을 풀기위한 효과적인 병렬 알고리즘)

  • Chae, Soo-Hoan;Lee, Jin
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.14 no.4
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    • pp.388-397
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    • 1989
  • This paper describes an intelligent iterative parallel algorithm for solving large sparse linear systems of equations, and proposes a ststic dataflow computer architechture for the implementation of the algorithm. Implemented with the Jacobi interative method, the intelligent algorithm reduces the parallel execution time by reducing the individual inner product operation time.

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Exploration of an Optimal Two-Dimensional Multi-Core System for Singular Value Decomposition (특이치 분해를 위한 최적의 2차원 멀티코어 시스템 탐색)

  • Park, Yong-Hun;Kim, Cheol-Hong;Kim, Jong-Myon
    • Journal of the Korea Society of Computer and Information
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    • v.19 no.9
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    • pp.21-31
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    • 2014
  • Singular value decomposition (SVD) has been widely used to identify unique features from a data set in various fields. However, a complex matrix calculation of SVD requires tremendous computation time. This paper improves the performance of a representative one-sided block Jacoby algorithm using a two-dimensional (2D) multi-core system. In addition, this paper explores an optimal multi-core system by varying the number of processing elements in the 2D multi-core system with the same 400MHz clock frequency and TSMC 28nm technology for each matrix-based one-sided block Jacoby algorithm ($128{\times}128$, $64{\times}64$, $32{\times}32$, $16{\times}16$). Moreover, this paper demonstrates the potential of the 2D multi-core system for the one-sided block Jacoby algorithm by comparing the performance of the multi-core system with a commercial high-performance graphics processing unit (GPU).

AN EFFICIENT ALGORITHM FOR EVALUATION OF OSCILLATORY INTEGRALS HAVING CAUCHY AND JACOBI TYPE SINGULARITY KERNELS

  • KAYIJUKA, IDRISSA;EGE, SERIFE M.;KONURALP, ALI;TOPAL, FATMA S.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.267-281
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    • 2022
  • Herein, an algorithm for efficient evaluation of oscillatory Fourier-integrals with Jacobi-Cauchy type singularities is suggested. This method is based on the use of the traditional Clenshaw-Curtis (CC) algorithms in which the given function is approximated by the truncated Chebyshev series, term by term, and the oscillatory factor is approximated by using Bessel function of the first kind. Subsequently, the modified moments are computed efficiently using the numerical steepest descent method or special functions. Furthermore, Algorithm and programming code in MATHEMATICA® 9.0 are provided for the implementation of the method for automatic computation on a computer. Finally, selected numerical examples are given in support of our theoretical analysis.

$H{\infty}$ CONTROL OF NONLINEAR SYSTEMS WITH NORM BOUNDED UNCERTAINTIES

  • Jang, S.;Araki, M.
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.412-415
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    • 1995
  • Previously obtained results of L$_{2}$-gain and H$_{\infty}$ control via state feedback of nonlinear systems are extended to a class of nonlinear system with uncertainties. The required information about the uncertainties is that the uncertainties are bounded in Euclidian norm by known functions of the system state. The conditions are characterized in terms of the corresponding Hamilton-Jacobi equations or inequalities (HJEI). An algorithm for finding an approximate local solution of Hamilton-Jacobi equation is given. This results and algorithm are illustrated on a numerical example..

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THE CHIRAL SUPERSTRING SIEGEL FORM IN DEGREE TWO IS A LIFT

  • Poor, Cris;Yuen, David S.
    • Journal of the Korean Mathematical Society
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    • v.49 no.2
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    • pp.293-314
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    • 2012
  • We prove that the Siegel modular form of D'Hoker and Phong that gives the chiral superstring measure in degree two is a lift. This gives a fast algorithm for computing its Fourier coefficients. We prove a general lifting from Jacobi cusp forms of half integral index t/2 over the theta group ${\Gamma}_1$(1, 2) to Siegel modular cusp forms over certain subgroups ${\Gamma}^{para}$(t; 1, 2) of paramodular groups. The theta group lift given here is a modification of the Gritsenko lift.

A Study on the Nonlinear and Linear Analysis of Microwave Diode Mixer (마이크로波 다이오드 混合器의 非線形 및 線形解析에 關한 硏究)

  • Park, Eui-Joon;Park, Cheong-Kee
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.26 no.4
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    • pp.7-15
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    • 1989
  • A technique is suggested which enables the large signal current and voltage waveforms to be determined for a GaAs Schottky-Barrier diode mixer by extracting the algorithm for the nonlinear circuit analysis from the Gauss-Jacobi relaxation and the application of the Harmonic Balance Technique. Both the nonlinear and linear steps of the analysis are included. This analysis permitts accurate determination of the conversion loss for microwave mixer and the computer simulation provides an method applicable to MMIC design. The validity of the nonlinear and linear analysis is confirmed by comparing the simulation results with experimental data of the conversion loss.

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Finite Element Analysis of Shape Rolling Process using Destributive Parallel Algorithms on Cray T3E (병렬 컴퓨터를 이용한 형상 압연공정 유한요소 해석의 분산병렬처리에 관한 연구)

  • Gwon, Gi-Chan;Yun, Seong-Gi
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.5 s.176
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    • pp.1215-1230
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    • 2000
  • Parallel Approaches using Cray T3E which is NIPP (Massively Parallel Processors) machine are presented for the efficient computation of the finite element analysis of 3-D shape rolling processes. D omain decomposition method coupled with parallel linear equation solver is used. Domain decomposition is applied for obtaining element tangent stifffiess matrices and residual vectors. Direct and iterative parallel algorithms are used for solving the linear equations. Direct algorithm is_parallel version of direct banded matrix solver. For iterative algorithms, the well-known preconditioned conjugate gradient solver with Jacobi preconditioner is also employed. Moreover a new effective iterative scheme with block inverse matrix preconditioner, which is named by present authors, is presented and its results are compared with the one using Jacobi preconditioner. PVM and MPI are used for message passing and synchronization between processors. The performance and efficiency of each algorithm is discussed and comparisons are made among different algorithms.

A DEEP LEARNING ALGORITHM FOR OPTIMAL INVESTMENT STRATEGIES UNDER MERTON'S FRAMEWORK

  • Gim, Daeyung;Park, Hyungbin
    • Journal of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.311-335
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    • 2022
  • This paper treats Merton's classical portfolio optimization problem for a market participant who invests in safe assets and risky assets to maximize the expected utility. When the state process is a d-dimensional Markov diffusion, this problem is transformed into a problem of solving a Hamilton-Jacobi-Bellman (HJB) equation. The main purpose of this paper is to solve this HJB equation by a deep learning algorithm: the deep Galerkin method, first suggested by J. Sirignano and K. Spiliopoulos. We then apply the algorithm to get the solution to the HJB equation and compare with the result from the finite difference method.