• Title/Summary/Keyword: spectral norm

Search Result 35, Processing Time 0.025 seconds

JACOBI SPECTRAL GALERKIN METHODS FOR VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNEL

  • Yang, Yin
    • Bulletin of the Korean Mathematical Society
    • /
    • v.53 no.1
    • /
    • pp.247-262
    • /
    • 2016
  • We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

ON THE g-CIRCULANT MATRICES

  • Bahsi, Mustafa;Solak, Suleyman
    • Communications of the Korean Mathematical Society
    • /
    • v.33 no.3
    • /
    • pp.695-704
    • /
    • 2018
  • In this paper, firstly we compute the spectral norm of g-circulant matrices $C_{n,g}=g-Circ(c_0,c_1,{\cdots},c{_{n-1}})$, where $c_i{\geq}0$ or $c_i{\leq}0$ (equivalently $c_i{\cdot}c_j{\geq}0$). After, we compute the spectral norms, determinants and inverses of the g-circulant matrices with the Fibonacci and Lucas numbers.

Convergence Properties of a Spectral Density Estimator

  • Gyeong Hye Shin;Hae Kyung Kim
    • Communications for Statistical Applications and Methods
    • /
    • v.3 no.3
    • /
    • pp.271-282
    • /
    • 1996
  • this paper deal with the estimation of the power spectral density function of time series. A kernel estimator which is based on local average is defined and the rates of convergence of the pointwise, $$L_2$-norm; and; $L{\infty}$-norm associated with the estimator are investigated by restricting as to kernels with suitable assumptions. Under appropriate regularity conditions, it is shown that the optimal rate of convergence for 0$N^{-r}$ both in the pointwiseand $$L_2$-norm, while; $N^{r-1}(logN)^{-r}$is the optimal rate in the $L{\infty}-norm$. Some examples are given to illustrate the application of main results.

  • PDF

Multiview-based Spectral Weighted and Low-Rank for Row-sparsity Hyperspectral Unmixing

  • Zhang, Shuaiyang;Hua, Wenshen;Liu, Jie;Li, Gang;Wang, Qianghui
    • Current Optics and Photonics
    • /
    • v.5 no.4
    • /
    • pp.431-443
    • /
    • 2021
  • Sparse unmixing has been proven to be an effective method for hyperspectral unmixing. Hyperspectral images contain rich spectral and spatial information. The means to make full use of spectral information, spatial information, and enhanced sparsity constraints are the main research directions to improve the accuracy of sparse unmixing. However, many algorithms only focus on one or two of these factors, because it is difficult to construct an unmixing model that considers all three factors. To address this issue, a novel algorithm called multiview-based spectral weighted and low-rank row-sparsity unmixing is proposed. A multiview data set is generated through spectral partitioning, and then spectral weighting is imposed on it to exploit the abundant spectral information. The row-sparsity approach, which controls the sparsity by the l2,0 norm, outperforms the single-sparsity approach in many scenarios. Many algorithms use convex relaxation methods to solve the l2,0 norm to avoid the NP-hard problem, but this will reduce sparsity and unmixing accuracy. In this paper, a row-hard-threshold function is introduced to solve the l2,0 norm directly, which guarantees the sparsity of the results. The high spatial correlation of hyperspectral images is associated with low column rank; therefore, the low-rank constraint is adopted to utilize spatial information. Experiments with simulated and real data prove that the proposed algorithm can obtain better unmixing results.

ON SPECTRAL BOUNDEDNESS

  • Harte, Robin
    • Journal of the Korean Mathematical Society
    • /
    • v.40 no.2
    • /
    • pp.307-317
    • /
    • 2003
  • For linear operators between Banach algebras "spectral boundedness" is derived from ordinary boundedness by substituting spectral radius for norm. The interplay between this concept and some of its near relatives is conspicuous in a result of Curto and Mathieu.

A Modified Method Based on the Discrete Sliding Norm Transform to Reduce the PAPR in OFDM Systems

  • Salmanzadeh, R.;Mozaffari Tazehkand, B.
    • ETRI Journal
    • /
    • v.36 no.1
    • /
    • pp.42-50
    • /
    • 2014
  • Orthogonal frequency division multiplexing (OFDM) is a modulation technique that allows the transmission of high data rates over wideband radio channels subject to frequency selective fading by dividing the data into several narrowband and flat fading channels. OFDM has high spectral efficiency and channel robustness. However, a major drawback of OFDM is that the peak-to-average power ratio (PAPR) of the transmitted signals is high, which causes nonlinear distortion in the received data and reduces the efficiency of the high power amplifier in the transmitter. The most straightforward method to solve this problem is to use a nonlinear mapping algorithm to transform the signal into a new signal that has a smaller PAPR. One of the latest nonlinear methods proposed to reduce the PAPR is the $L_2$-by-3 algorithm, which is based on the discrete sliding norm transform. In this paper, a new algorithm based on the $L_2$-by-3 method is proposed. The proposed method is very simple and has a low complexity analysis. Simulation results show that the proposed method performs better, has better power spectral density, and is less sensitive to the modulation type and number of subcarriers than $L_2$-by-3.

SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS

  • Yang, Yin;Chen, Yanping;Huang, Yunqing
    • Journal of the Korean Mathematical Society
    • /
    • v.51 no.1
    • /
    • pp.203-224
    • /
    • 2014
  • We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Fredholm-Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

Generalized Norm Bound of the Algebraic Matrix Riccati Equation (대수리카티방정식의 해의 일반적 노음 하한)

  • Kang, Tae-Sam;Lee, Jang-Gyu
    • Proceedings of the KIEE Conference
    • /
    • 1992.07a
    • /
    • pp.296-298
    • /
    • 1992
  • Presented in this paper is a generalized norm bound for the continuous and discrete algebraic Riccati equations. The generalized norm bound provides a lower bound of the Riccati solutions specified by any kind of submultiplicative matrix norms including the spectral, Frobenius and $\ell_1$ norms.

  • PDF

NONCONFORMING SPECTRAL ELEMENT METHOD FOR ELASTICITY INTERFACE PROBLEMS

  • Kumar, N. Kishore
    • Journal of applied mathematics & informatics
    • /
    • v.32 no.5_6
    • /
    • pp.761-781
    • /
    • 2014
  • An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.