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...

We compute the operator norm of real-quadratic polynomials Volterra operator. This is used to test whether Crouzeix conjecture holds for

In convergence analysis of finite element methods for singularly perturbed reaction–diffusion problems, balanced norms have been successfully introduced to replace standard energy so that layers can be captured. this article, we focus on the in a norm Bakhvalov-type rectangular meshes. order achieve our goal, novel interpolation operator, which consists local $$L^2$$ projection operator and Lag...

In this paper we study the subdifferential set of an operator. We give possible relation operator to that its value, at a point where attains norm.

A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into l∞ defined by