We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.doi:10.48550/arXiv.1104.2076Malik Magdon-Ismail...
Example 4: Compute Maximum Modulus Norm of Matrix This example explains how to compute the maximum modulus norm of a matrix: norm(my_mat, type="M")# Maximum modulus# [1] 10 Example 5: Compute Spectral Norm / 2-Norm of Matrix
, n, and let ‖‖ denote the spectral norm. In a previous paper it was proved that Here we prove that Each inequality implies, and is equivalent to, the triangle inequality for the recently constructed spherical distance of a projective matrix space, and the validity of either of these ...
The spectral norm of a matrix M is defined as the largest singular value of M, denoted by ||M||s. For some classical results used in the proof, we may refer to Nikiforov's pioneering paper [48]. Lemma 2.1 ([46]) If M is a nonzero Hermitian n×n matrix, thenSM≥|tr(M3)tr(...
In particular, we determine the oriented trees for which the trace norm of Aα matrix attains minimum. We obtain a lower bound for the α spectral norm σ1α(D) of digraphs and characterize the extremal digraphs. As an application of this result, we obtain an upper bound for the α ...
For c = (1,0,…, 0) they are reduced to the classical eigenpolygon, numerical range, spectral radius, numerical radius and spectral norm of A. We say that the matrix A is c-spectral if pc (A) =rc (A)c-radial if pc (A) = ||A|| c , and c-convex if Pc (A) = Wc (A...
一、Spectral Norm Regularization 1.1谱范数的提出 首先,作者提出了衡量扰动的计算公式: 该公式衡量当x发生一定程度变化时,y变化的大小。根据上述公式我们定义了谱范数,对于一个矩阵A 根据数学推导可以得出,A的谱范数等于其最大的特征值【1】。我们希望Y函数尽可能的平滑就需要约束A的谱范数尽可能地小。
In this paper, both well-known and new properties of the spectral abscissa and the logarithmic norm are described. In addition to well-known formulas for the norm of a matrix and for its logarithmic norm in cubic, octahedral, spherical norms, various estimates for these quantities in an arbitr...
computation of the cross-correlation. Both volumes are first transformed into the Fourier space using the FFT algorithm [104], after which the cross-correlation simplifies to a matrix multiplication [105]. The output is then transformed back with an inverse FFT. More details are given in Sect....
We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spectral norm regularization, which penalizes the high spectral norm of weight ...