• Title/Summary/Keyword: conjugate gradient(CG)

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Conjugate Gradient Least-Squares Algorithm for Three-Dimensional Magnetotelluric Inversion (3차원 MT 역산에서 CG 법의 효율적 적용)

  • Kim, Hee-Joon;Han, Nu-Ree;Choi, Ji-Hyang;Nam, Myung-Jin;Song, Yoon-Ho;Suh, Jung-Hee
    • Geophysics and Geophysical Exploration
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    • v.10 no.2
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    • pp.147-153
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    • 2007
  • The conjugate gradient (CG) method is one of the most efficient algorithms for solving a linear system of equations. In addition to being used as a linear equation solver, it can be applied to a least-squares problem. When the CG method is applied to large-scale three-dimensional inversion of magnetotelluric data, two approaches have been pursued; one is the linear CG inversion in which each step of the Gauss-Newton iteration is incompletely solved using a truncated CG technique, and the other is referred to as the nonlinear CG inversion in which CG is directly applied to the minimization of objective functional for a nonlinear inverse problem. In each procedure we only need to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector, significantly reducing the computational requirements needed to do large-scale inversion.

Radiation Analysis of a Finite Microstrip Antenna Structure Using the CG-FFT Method : Volume Formulation (유한한 마이크로스트립 안테나구조에서 CG-FFT 방법을 이용한 복사 해석)

  • 손창우;이철훈김종규조영기
    • Proceedings of the IEEK Conference
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    • 1998.10a
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    • pp.343-346
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    • 1998
  • In this paper a radiation problem for a finite microstrip antenna structure is analyzed. For the analysis of finite structures we utilize the equivalent volume current. Intergral equation for the unknown equivalent volume current induced on a finite microstrip structure is derived and solved by the use of conjugate gradient-fast fourier. transform (CG-FFT) method. Some numerical examples are radiation patterns derived by the equivalent volume current solved by the conjugate gradient-fast fourier transform.

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Hybrid of SA and CG Methods for Designing the Ka-Band Group-Delay Equalized Filter (Ka-대역 군지연-등화 여파기용 SA 기법과 CG 기법의 하이브리드 설계 기법)

  • Kahng, Sungtek
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.15 no.8
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    • pp.775-780
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    • 2004
  • This paper describes the realization of the Ka-band group-delay equalized filter desisted with the help of a new hybrid method of Simulated Annealing(SA) and Conjugate Gradient(CG), to be employed by the multi-channel Input Multiplexer for a satellite use, each channel of which comprises a channel filter and a group-delay equalizer. The SA and CG find circuit parameters of an 8th order elliptic function filter and a 2-pole equalizer, respectively. Measurement results demonstrate that the performances of the designed component meet the specifications, and validate the design methods.

A LOGARITHMIC CONJUGATE GRADIENT METHOD INVARIANT TO NONLINEAR SCALING

  • Moghrabi, I.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.8 no.2
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    • pp.15-21
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    • 2004
  • A Conjugate Gradiant (CG) method is proposed for unconstained optimization which is invariant to a nonlinear scaling of a strictly convex quadratic function. The technique has the same properties as the classical CG-method when applied to a quadratic function. The algorithm derived here is based on a logarithmic model and is compared to the standard CG method of Fletcher and Reeves [3]. Numerical results are encouraging and indicate that nonlinear scaling is promising and deserves further investigation.

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A NEW CONJUGATE GRADIENT MINIMIZATION METHOD BASED ON EXTENDED QUADRATIC FUNCTIONS

  • Moghrabi, Issam.A.R.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.8 no.2
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    • pp.7-13
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    • 2004
  • A Conjugate Gradient (CG) algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for the minimization of general nonlinear functions. It compares favorably in numerical tests with the original Dixon algorithm on which the new algorithm is based.

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THE STEEPEST DESCENT METHOD AND THE CONJUGATE GRADIENT METHOD FOR SLIGHTLY NON-SYMMETRIC, POSITIVE DEFINITE MATRICES

  • Shin, Dong-Ho;Kim, Do-Hyun;Song, Man-Suk
    • Communications of the Korean Mathematical Society
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    • v.9 no.2
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    • pp.439-448
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    • 1994
  • It is known that the steepest descent(SD) method and the conjugate gradient(CG) method [1, 2, 5, 6] converge when these methods are applied to solve linear systems of the form Ax = b, where A is symmetric and positive definite. For some finite difference discretizations of elliptic problems, one gets positive definite matrices that are almost symmetric. Practically, the SD method and the CG method work for these matrices. However, the convergence of these methods is not guaranteed theoretically. The SD method is also called Orthores(1) in iterative method papers. Elman [4] states that the convergence proof for Orthores($\kappa$), with $\kappa$ a positive integer, is not heard. In this paper, we prove that the SD method and the CG method converge when the $\iota$$^2$ matrix norm of the non-symmetric part of a positive definite matrix is less than some value related to the smallest and the largest eigenvalues of the symmetric part of the given matrix.(omitted)

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Optimizations of Multi-hop Cooperative Molecular Communication in Cylindrical Anomalous-Diffusive Channel

  • Xuancheng Jin;Zhen Cheng;Zhian Ye;Weihua Gong
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.18 no.4
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    • pp.1075-1089
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    • 2024
  • In this paper, the optimizations of multi-hop cooperative molecular communication (CMC) system in cylindrical anomalous-diffusive channel in three-dimensional enviroment are investigated. First, we derive the performance of bit error probability (BEP) of CMC system under decode-and-forward relay strategy. Then for achieving minimum average BEP, the optimization variables are detection thresholds at cooperative nodes and destination node, and the corresponding optimization problem is formulated. Furthermore, we use conjugate gradient (CG) algorithm to solve this optimization problem to search optimal detection thresholds. The numerical results show the optimal detection thresholds can be obtained by CG algorithm, which has good convergence behaviors with fewer iterations to achieve minimized average BEP compared with gradient decent algorithm and Bisection method which are used in molecular communication.

A Study of Spectral Domain Electromagnetic Scattering Analysis Applying Wavelet Transform (웨이블릿을 이용한 파수영역 전자파 산란 해석법 연구)

  • 빈영부;주세훈;이정흠;김형동
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.11 no.3
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    • pp.337-344
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    • 2000
  • The wavelet analysis technique is applied in the spectral domain to efficiently represent the multi-scale features of the impedance matrices. In this scheme, the 2-D quadtree decomposition (applying the wavelet transform to only the part of the matrix) method often used in image processing area is applied for a sparse moment matrix. CG(Conjugate-Gradient) method is also applied for saving memory and computation time of wavelet transformed moment matrix. Numerical examples show that for rectangular cylinder case the non-zero elements of the transformed moment matrix grows only as O($N^{1.6}$).

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Iterative Least-Squares Method for Velocity Stack Inversion - Part B: CGG Method (속도중합역산을 위한 반복적 최소자승법 - Part B: CGG 방법)

  • Ji Jun
    • Geophysics and Geophysical Exploration
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    • v.8 no.2
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    • pp.170-176
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    • 2005
  • Recently the velocity stack inversion is having many attentions as an useful way to perform various seismic data processing. In order to be used in various seismic data processing, the inversion method used should have properties such as robustness to noise and parsimony of the velocity stack result. The IRLS (Iteratively Reweighted Least-Squares) method that minimizes ${L_1}-norm$ is the one used mostly. This paper introduce another method, CGG (Conjugate Guided Gradient) method, which can be used to achieve the same goal as the IRLS method does. The CGG method is a modified CG (Conjugate Gradient) method that minimizes ${L_1}-norm$. This paper explains the CGG method and compares the result of it with the one of IRSL methods. Testing on synthetic and real data demonstrates that CGG method can be used as an inversion method f3r minimizing various residual/model norms like IRLS methods.

CUDA-based Parallel Bi-Conjugate Gradient Matrix Solver for BioFET Simulation (BioFET 시뮬레이션을 위한 CUDA 기반 병렬 Bi-CG 행렬 해법)

  • Park, Tae-Jung;Woo, Jun-Myung;Kim, Chang-Hun
    • Journal of the Institute of Electronics Engineers of Korea CI
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    • v.48 no.1
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    • pp.90-100
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    • 2011
  • We present a parallel bi-conjugate gradient (Bi-CG) matrix solver for large scale Bio-FET simulations based on recent graphics processing units (GPUs) which can realize a large-scale parallel processing with very low cost. The proposed method is focused on solving the Poisson equation in a parallel way, which requires massive computational resources in not only semiconductor simulation, but also other various fields including computational fluid dynamics and heat transfer simulations. As a result, our solver is around 30 times faster than those with traditional methods based on single core CPU systems in solving the Possion equation in a 3D FDM (Finite Difference Method) scheme. The proposed method is implemented and tested based on NVIDIA's CUDA (Compute Unified Device Architecture) environment which enables general purpose parallel processing in GPUs. Unlike other similar GPU-based approaches which apply usually 32-bit single-precision floating point arithmetics, we use 64-bit double-precision operations for better convergence. Applications on the CUDA platform are rather easy to implement but very hard to get optimized performances. In this regard, we also discuss the optimization strategy of the proposed method.