In this work‎, ‎an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$‎ ‎and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$‎ ‎where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$‎, ‎$mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$‎, ‎$ma...

The multiplicative perturbation bounds for weighted unitary polar factor are considered in the weighted unitary invariant norm, weighted spectral norm, and weighted Frobenius norm in this paper. As the special cases, new bounds for subunitary and unitary polar factor are also derived. These new bounds improve the corresponding results published recently to some extent. Mathematics subject class...

We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix size is much larger than the rank of the signal matrix to be recovered, and the signal-to-noise ratio of the low-rank piece stays constant. For a variety of...

Color image denoising is frequently encountered in various processing and computer vision tasks. One traditional strategy to convert the RGB a less correlated color space denoise each channel of new separately. However, such can not fully exploit information between channels inadequate obtain satisfactory results. To address this issue, paper proposes multi-channel optimization model for under ...

In the last lecture we discussed how distributional JL implies Gordon's theorem, and began our discussion of sparse JL. We wrote Πx 2 = σ T A T x A x σ and bounded the expression using Hanson-Wright in terms of the Frobenius norm. In this lecture we'll bound that Frobenius norm and then discuss applications to fast nearest neighbors. Note that we defined B x = A T x A x as the center of the pro...

Approximate inverses, based on Frobenius norm minimization, of real nonsingular matrices are analyzed from a purely theoretical point of view. In this context, this paper provides several sufficient conditions, that assure us the possibility of improving (in the sense of the Frobenius norm) some given approximate inverses. Moreover, the optimal approximate inverses of matrix A ∈ R, among all ma...

In this article some new results are presented about planar quadrangle quality measures. On the one hand, a modi cation of the triangle quality measure based on the Frobenius norm is proposed, in order to comply with the case where the reference element is no longer equilateral, but a right isosceles triangle. Provided this modi cation, a natural use of the Frobenius norm for quadrangular eleme...

We consider the real ε-pseudospectrum of a real square matrix, which is the set of eigenvalues of all real matrices that are ε-close to the given matrix, where closeness is measured in either the 2-norm or the Frobenius norm. We characterize extremal points and compare the situation with that for the complex ε-pseudospectrum. We present differential equations for rank-1 and rank2 matrices for t...

Low Rank Representation (LRR) intends to find the representation with lowest-rank of a given data set, which can be formulated as a rank minimization problem. Since the rank operator is non-convex and discontinuous, most of the recent works use the nuclear norm as a convex relaxation. This letter theoretically shows that under some conditions, Frobenius-norm-based optimization problem has an un...

in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...