• Title/Summary/Keyword: Singular

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ILL-VERSUS WELL-POSED SINGULAR LINEAR SYSTEMS: SCOPE OF RANDOMIZED ALGORITHMS

  • Sen, S.K.;Agarwal, Ravi P.;Shaykhian, Gholam Ali
    • Journal of applied mathematics & informatics
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    • v.27 no.3_4
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    • pp.621-638
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    • 2009
  • The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

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Power Efficient Precoding by Reducing the Effect of the Largest Singular Value of channel Inverse Matrix (채널 역변환 매트릭스의 가장 큰 싱귤러 값 영향을 줄이는 다중 사용자 프리코딩)

  • Ro, Se Yong;Yang, Hyun Wook;Chong, Jong Wha
    • Journal of Korea Society of Digital Industry and Information Management
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    • v.8 no.4
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    • pp.115-120
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    • 2012
  • In multi-user multi-input multi-output (MU-MIMO) system, zero forcing beamforming (ZFB) is regarded as a realistic solution for transmitting scheme due to its low complexity and simple structure. However, ZFB shows a significant performance degradation when channel matrix has large condition number. In this case, the largest singular value of the channel inversion matrix has a dominant effect on transmit power. In this paper, we propose a perturbation method for reducing an effect of the dominant singular value. In the proposed algorithm, channel inverse matrix is first decomposed by SVD for the transmit signal to be expressed as a combination of singular vectors. Then, the transmit signal is perturbed to reduce the coefficient of the singular vector corresponding to the largest singular value. When a number of transmit antennas is 4, the simulation results of this paper shows that the proposed method shows 8dB performance enhancement at 10-3 uncoded bit error rate (BER) compared with conventional ZFB. Also, the simulation results show that the proposed method provides a comparable performance to Tomlinson-Harashima Precoding (THP) with much lower complexity.

Tool-trajectory Error at the Singular Area of Five-axis Machining - Part I: Trajectory Error Modeling - (5축 가공의 특이영역에서 공구궤적 오차 - Part I: 궤적오차 모델링 -)

  • So, Bum-Sik;Jung, Yoong-Ho;Yun, Jae-Deuk
    • Korean Journal of Computational Design and Engineering
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    • v.14 no.1
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    • pp.18-24
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    • 2009
  • This paper proposes an analytical method of evaluating the maximum error by modeling the exact tool path for the tool traverse singular region in five-axis machining. It is known that the NC data from the inverse kinematics transformation of 5-axis machining can generate singular positions where incoherent movements of the rotary axes can appear. These lead to unexpected errors and abrupt operations, resulting in scoring on the machined surface. To resolve this problem, previous methods have calculated several tool positions during a singular operation, using inverse kinematics equations to predict tool trajectory and approximate the maximum error. This type of numerical approach, configuring the tool trajectory, requires much computation time to obtain a sufficient number of tool positions in a region. We have derived an analytical equation for the tool trajectory in a singular area by modeling the tool operation into a linear and a nonlinear part that is a general form of the tool trajectory in the singular area and that is suitable for all types of five-axis machine tools. In addition, we have evaluated the maximum tool-path error exactly, using our analytical model. Our algorithm can be used to modify NC data, making the operation smoother and bringing any errors to within tolerance.

QUASILINEARIZATION FOR SECOND ORDER SINGULAR BOUNDARY VALUE PROBLEMS WITH SOLUTIONS IN WEIGHTED SPACES

  • Devi, J.Vasundhara;Vatsala, A.S.
    • Journal of the Korean Mathematical Society
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    • v.37 no.5
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    • pp.823-833
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    • 2000
  • In this paper, we develop the method of quasilinearization comvined with the methos of upper and lower solutions for singular second order boundary value problems in weighted spaces. The sequences constructed converge uniformly and monotonically to the unique of the second singular order boundary value problem. Further we prove the rate of convergence is quadratic.

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Hankel approximation of commensurate input delay systems (복수 입력 시간지연 시스템의 한켈 근사화)

  • 황이철;태전쾌인
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.1452-1455
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    • 1997
  • This paper studies the problem of approximating commensurate input delay sustems by finite dimensional systems based on the Hankel singular values. I is shown that the Gankel singular values are solutions a trancendental equation and the Hankel singular vectors are obtained form the kernel of the matrix. The computaioin is carried out in state spae framework. Once singular values and vectors are calcualted, finite dimensional approximated systems are constructed using stadnard linear system computational tools. An example is included.

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Effect Analysis of Generator Dropping Using Wavelet Singular Value Decomposition (발전기 탈락 시 Wavelet Transform과 Singular Value Decomposition을 이용한 특성 분석)

  • Noh, Chul-Ho;Kim, Won-Ki;Han, Jun;Kim, Chul-Hwan
    • Proceedings of the KIEE Conference
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    • 2011.07a
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    • pp.49-50
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    • 2011
  • 본 논문에서는 WT(Wavelet Transform)와 SVD(Singular Value Decomposition)를 함께 사용한 WSVD(Wavelet Singular Value Decomposition)를 이용하여 발전기 탈락 시의 전압 변동 특성을 분석하였다. WSVD 특성 분석을 위해 부산 지역의 345kV급 송전계통을 EMTP-RV로 모델링하였으며, 이 계통모델에서 발전기 탈락을 모의하였다. MATLAB을 통해 이 때 측정된 전압의 WSVD를 계산하여 발전기 탈락에 따른 특성을 분석하였다.

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QUANTITATIVE WEIGHTED BOUNDS FOR THE VECTOR-VALUED SINGULAR INTEGRAL OPERATORS WITH NONSMOOTH KERNELS

  • Hu, Guoen
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.6
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    • pp.1791-1809
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    • 2018
  • Let T be the singular integral operator with nonsmooth kernel which was introduced by Duong and McIntosh, and $T_q(q{\in}(1,{\infty}))$ be the vector-valued operator defined by $T_qf(x)=({\sum}_{k=1}^{\infty}{\mid}T\;f_k(x){\mid}^q)^{1/q}$. In this paper, by proving certain weak type endpoint estimate of L log L type for the grand maximal operator of T, the author establishes some quantitative weighted bounds for $T_q$ and the corresponding vector-valued maximal singular integral operator.

EXISTENCE OF THE SOLUTIONS FOR THE SINGULAR POTENTIAL ELLIPTIC SYSTEM

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.20 no.1
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    • pp.107-116
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    • 2012
  • We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

REAL VERSION OF PALEY-WIENER-SCHWARTZ THEOREM FOR ULTRADISTRIBUTIONS WITH ULTRADIFFERENTIABLE SINGULAR SUPPORT

  • Cho, Jong-Gyu;Kim, Kwang-Whoi
    • Bulletin of the Korean Mathematical Society
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    • v.36 no.3
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    • pp.483-493
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    • 1999
  • We extend the Paley-Wiener-Schwartz theorem to the space of ultradistributions with respect to ultradifferentiable singular support and obtain its real version. That is, we obtain the growth condition in some tubular neighborhood of n of the Fourier transform of ultradistributions of Roumieu (or Beurling) type with ultradifferentiable singular support contained in a ball centered at the origin, and its real version.

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