R. Mathias, The spectral norm of a nonnegative matrix, Linear Algebra Appl. 131 (1990) 269-284.Mathias, R: The spectral norm of a nonnegative matrix. Linear Algebra Appl. 139, 269-284 (1990)R. Mathias, The spectral norm of a nonnegative matrix, Linear Algebra Appl., 139 (1990), ...
A multi-dimensional state monitoring matrix is built using the measured current data. The spectral norm ratio coefficient is constructed based on the 2-norm to lower the complexity of the multi-dimensional state monitoring matrix and quantify the difference in state changes before and after the ...
Spectral_norm() does not normalize the original weight matrix; The first two prints will give the same weight matrix; If we compute sigma using members weight_u and weight_v and then normalize original weight matrix, it will produce a different weight matrix; ...
∣∣is a matrix norm. Basically, it is a measure of how the eigenvalues of the original system vary in response to small perturbations. However, the above definition, which was used in connection with non-Hermitian photonics in ref.56is difficult to apply. Another equivalent, yet more ...
err=norm(xmxh)/norm(x); disp(sprintf('L2 normof relative reconstruction error = %g',err)); % I observe 8E-16 for both odd and even win length cases -josfigure(2); clf; %n1 = round(L/8); n2 = n1+100; n1 = 1; n2 = n1+3000; ...
the computation of the numerical solution reduces to solving a linear discrete problem identified by a matrixX_n. The size ofX_ngrows asnincreases, i.e., as the mesh is progressively refined, and ultimately we are left with a sequence of matricesX_nsuch that\textrm{size}(X_n)\rightarrow...
Using the Laplacian matrix in equation (2), Hall’s energy can be denoted asE=xTLxxTLx. The trivial solution,xx=0, can be eliminated by requiring the coordinates vector norm to be nonzero, i.e.,xTxxTx=c. As the coordinates can be arbitrarily scaled, the constantccan be set to 1:xT...
Faced with this embarrassment of riches, we opt for the spectral methods. It is common to use spectral discretization in the numerical Stability and error estimates To study the stability and error estimates for the proposed methods, we introduce the discrete l2-norm ‖⋅‖l2 on the interval ...
They bounded the spectral radius of a random symmetric matrix, and their result has been improved by Vu [30] subsequently. These results were extended to sparse random graphs [15], [21]. Ding et al. [14] studied the largest eigenvalue and the spectral norm of the adjacency matrix of ...
本文在[1]与[2]的基础上研究了数值半径,矩阵的谱范数和矩阵范数之间的关系,又给出了一些新的不等式。 In the paper we study numerical radius, spectral norm of matrix, matrix norm and theirs relations...