Inequalities related to Schatten norm
نویسندگان
چکیده
In this paper, we investigate the known operator inequalities for p-Schatten norm and obtain some refinements of these when parameters taking values in different regions. Let A1,...,An, B1,..., Bn ? Bp(H) such that ?ni,j=1Ai*Bj=0. Then p 2, 21/p-?/4n3/p-?/4-1/2(?ni=1 ||Ai||4/?p + ?ni=1 ||Bi||4/?p )?/4 n2/p-1/2||?ni=1 |Ai|2 |Bi|2||1/2 p/2 n2/p-2/?(?ni,j=1 ||Ai Bj||?p)1/?. For 0 < > are reversed. Moreover, get applications our results.
منابع مشابه
Tractable and Scalable Schatten Quasi-Norm Approximations for Rank Minimization
The Schatten quasi-norm was introduced tobridge the gap between the trace norm andrank function. However, existing algorithmsare too slow or even impractical for large-scale problems. Motivated by the equivalencerelation between the trace norm and its bilin-ear spectral penalty, we define two tractableSchatten norms, i.e. the bi-trace and tri-tracenorms, and prov...
متن کاملLow-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization
As an emerging machine learning and information retrieval technique, the matrix completion has been successfully applied to solve many scientific applications, such as collaborative prediction in information retrieval, video completion in computer vision, etc. The matrix completion is to recover a low-rank matrix with a fraction of its entries arbitrarily corrupted. Instead of solving the popul...
متن کاملConvex Tensor Decomposition via Structured Schatten Norm Regularization
We study a new class of structured Schatten norms for tensors that includes two recently proposed norms (“overlapped” and “latent”) for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we analyze the performance of “latent” approach for tensor decomposition, which was empirically found to perform better than the “overlapped” approach in s...
متن کاملA Unified Convex Surrogate for the Schatten-p Norm
The Schatten-p norm (0 < p < 1) has been widely used to replace the nuclear norm for better approximating the rank function. However, existing methods are either 1) not scalable for large scale problems due to relying on singular value decomposition (SVD) in every iteration, or 2) specific to some p values, e.g., 1/2, and 2/3. In this paper, we show that for any p, p1, and p2 > 0 satisfying 1/p...
متن کاملScalable Algorithms for Tractable Schatten Quasi-Norm Minimization
The Schatten-p quasi-norm (0<p<1) is usually used to replace the standard nuclear norm in order to approximate the rank function more accurately. However, existing Schattenp quasi-norm minimization algorithms involve singular value decomposition (SVD) or eigenvalue decomposition (EVD) in each iteration, and thus may become very slow and impractical for large-scale problems. In this paper, we fi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Filomat
سال: 2021
ISSN: ['2406-0933', '0354-5180']
DOI: https://doi.org/10.2298/fil2113495g