• Title/Summary/Keyword: QMR

Search Result 11, Processing Time 0.033 seconds

AN ITERATIVE METHOD FOR SYMMETRIC INDEFINITE LINEAR SYSTEMS

  • Walker, Homer-F.;Yi, Su-Cheol
    • Communications of the Korean Mathematical Society
    • /
    • v.19 no.2
    • /
    • pp.375-388
    • /
    • 2004
  • For solving symmetric systems of linear equations, it is shown that a new Krylov subspace method can be obtained. The new approach is one of the projection methods, and we call it the projection method for convenience in this paper. The projection method maintains the residual vector like simpler GMRES, symmetric QMR, SYMMLQ, and MINRES. By studying the quasiminimal residual method, we show that an extended projection method and the scaled symmetric QMR method are equivalent.

ORTHOGONALIZATION PROCESS USING SYSTEMS

  • Yi, Su-Cheol
    • East Asian mathematical journal
    • /
    • v.15 no.2
    • /
    • pp.345-354
    • /
    • 1999
  • Orthogonalization can be done by the well known Gram-Schmidt process or by using Householder transformations. In this paper, we introduced an alternative process using linear systems.

  • PDF

PRECONDITIONED ITERATIVE METHOD FOR PETROV-GALERKIN PROCEDURE

  • Chung, Seiyoung;Oh, Seyoung
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.10 no.1
    • /
    • pp.57-70
    • /
    • 1997
  • In this paper two preconditioned GMRES and QMR methods are applied to the non-Hermitian system from the Petrov-Galerkin procedure for the Poisson equation and compared to each other. To our purpose the ILUT and the SSOR preconditioners are used.

  • PDF

NUMERICAL IMPLEMENTATION OF THE QMR ALGORITHM BY USING DISCRETE STOCHASTIC ARITHMETIC

  • TOUTOUNIAN FAEZEH;KHOJASTEH SALKUYEH DAVOD;ASADI BAHRAM
    • Journal of applied mathematics & informatics
    • /
    • v.17 no.1_2_3
    • /
    • pp.457-473
    • /
    • 2005
  • In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary to decide whether to construct the Lanczos vectors $v_{n+l}\;and\;w{n+l}$ as regular or inner vectors. For a regular step it is necessary that $D_k\;=\;W^{T}_{k}V_{k}$ is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix $D_k$, ${\sigma}_min(D_k)$, is computed and an inner step is performed if $\sigma_{min}(D_k)<{\epsilon}$, where $\epsilon$ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance $\epsilon$. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.

Analysis of 3D Microwave Oven Using Finite Element Method (전자렌지 캐비티의 전자파 해석)

  • Park, Kweong-Soo;Kim, Gweon-Jib;Shon, Jong-Chull;Kim, Sang-Gweon;Park, Yoon-Ser
    • Proceedings of the KIEE Conference
    • /
    • 1996.07c
    • /
    • pp.1753-1755
    • /
    • 1996
  • This paper presents an analysis of the 3D microwave oven considering its forming. The results were compared with experimental data. Finite Element Method(FEM) using edge clement is employed for the analysis. For solving the large sparse system matrix equation was solved using the parallelized QMR method. Analysis of the 3d cavity has troublesome difficulties such as spurious solutions, too many memory and long computation time. We overcome this difficulties by using edge clement for spurious solutions and the parallelized QMR method by the aid of Paralle Virtual Machine(PVM) for the memory and computation time.

  • PDF

AN ALGORITHM FOR SYMMETRIC INDEFINITE SYSTEMS OF LINEAR EQUATIONS

  • YI, SUCHEOL
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.3 no.2
    • /
    • pp.29-36
    • /
    • 1999
  • It is shown that a new Krylov subspace method for solving symmetric indefinite systems of linear equations can be obtained. We call the method as the projection method in this paper. The residual vector of the projection method is maintained at each iteration, which may be useful in some applications.

  • PDF

Virtual Source and Flooding-Based QoS Unicast and Multicast Routing in the Next Generation Optical Internet based on IP/DWDM Technology (IP/DWDM 기반 차세대 광 인터넷 망에서 가상 소스와 플러딩에 기초한 QoS 제공 유니캐스트 및 멀티캐스트 라우팅 방법 연구)

  • Kim, Sung-Un;Park, Seon-Yeong
    • Journal of Korea Multimedia Society
    • /
    • v.14 no.1
    • /
    • pp.33-43
    • /
    • 2011
  • Routing technologies considering QoS-based hypermedia services have been seen as a crucial network property in next generation optical Internet (NGOI) networks based on IP/dense-wavelength division multiplexing (DWDM). The huge potential capacity of one single fiber. which is in Tb/s range, can be exploited by applying DWDM technology which transfers multiple data streams (classified and aggregated IP traffics) on multiple wavelengths (classified with QoS-based) simultaneously. So, DWDM-based optical networks have been a favorable approach for the next generation optical backbone networks. Finding a qualified path meeting the multiple constraints is a multi-constraint optimization problem, which has been proven to be NP-complete and cannot be solved by a simple algorithm. The majority of previous works in DWDM networks has viewed heuristic QoS routing algorithms (as an extension of the current Internet routing paradigm) which are very complex and cause the operational and implementation overheads. This aspect will be more pronounced when the network is unstable or when the size of network is large. In this paper, we propose a flooding-based unicast and multicast QoS routing methodologies(YS-QUR and YS-QMR) which incur much lower message overhead yet yields a good connection establishment success rate. The simulation results demonstrate that the YS-QUR and YS-QMR algorithms are superior to the previous routing algorithms.

Heating simulations of the pancake in the simplified 3D microwave oven (간략화된 Cavity내부의 Pancake 가열 시뮬레이션)

  • Lee, Pyeong-Hwa;Cheon, Chang-Yul;Lee, Seung-Woo;Hahn, Song-Yop;Cho, Kyu-Wan;Kim, Eung-Su;Jeong, Bong-Sik;Kim, Hyun-Jung
    • Proceedings of the KIEE Conference
    • /
    • 1996.07c
    • /
    • pp.1741-1743
    • /
    • 1996
  • This paper presents simulations of the pancake in the simplified 3D microwave oven. The results were compared with experimental data. For the comparison we used infrared photography of the heated pancake and electric field distribution obtained by simulation. Finite Element Method (FEM) using edge element is employed for the simulation. For solving the large sparse system parallelled QMR method was used.

  • PDF

Parallel Linear Solver under PVM for Electric Machine Design (전기기계 설계용 병렬솔버 개발)

  • Kim, Hyung-Soo;Kim, Hyoung-Joong;Choi, Kyung;Lee, Hyang-Beom;Jung, Hyun-Kyo;Hahn, Song-Yop
    • Proceedings of the KIEE Conference
    • /
    • 1995.11a
    • /
    • pp.12-14
    • /
    • 1995
  • 전기기계의 설계시에 얻어지는 대형 선형방정식을 풀기 위해서는 엄청난 메모리가 필요하고 계산시간이 요구된다는 점을 고려해야 한다. 병렬계산은 이러한 문제를 해결할 수 있다. 우리는 PVM 환경에서 병렬계산이 가능한 솔비를 설계하였다. 선형방정식을 푸는 방법으로 QMR을 이용하였으며, 수렴속도를 향상시키기 위하여 대각 프리컨디셔너를 사용하였다. 실행 결과는 본 논문에서 구현한 솔비가 실제로 발생하는 문제에 대하여 아주 훌륭하게 동작하는 것을 보여준다.

  • PDF

Dual-Wideband Bandpass Filter Using Distributed Composite Right/Left-Handed Transmission Line Quad-Mode Resonators (분산 CRLH 전송선로 4중 모드 공진기를 이용한 이중-광대역 대역통과 여파기 설계)

  • Sung, Gyuje;Kim, Young
    • Journal of Advanced Navigation Technology
    • /
    • v.21 no.1
    • /
    • pp.84-89
    • /
    • 2017
  • This paper presents a dual-wideband bandpass filter (BPF) with high band-to-band isolation and skirt selectivity using distributed composite right/left-handed (CRLH) transmission line (TL) quad-mode resonators (QMRs). The results of the proposed distributed CRLH TL unit cell analysis are used to establish the scattering parameters and the resonance frequencies of the QMR constituting the dual-wideband BPF. A novel dual-wideband bandpass filter is designed and fabricated, using the derived scattering characteristics. The measured results show that the fabricated dual-wideband bandpass filter has an insertion loss of less than 1.08dB in the lower band, and of 2.01dB in the upper band, a bandwidth of 2.8-5.52GHz and 9.68-12.26GHz, and a band-to-band isolation of more than 38dB, from 6.34-8.42GHz.