in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...

The low-rank matrix recovery is an important machine learning research topic with various scientific applications. Most existing low-rank matrix recovery methods relax the rank minimization problem via the trace norm minimization. However, such a relaxation makes the solution seriously deviate from the original one. Meanwhile, most matrix recovery methods minimize the squared prediction errors ...

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...

In this paper, we theoretically investigate the low-rank matrix recovery problem in context of unconstrained regularized nuclear norm minimization (RNNM) framework. Our theoretical findings show that, RNNM method is able to provide a robust any X (not necessary be exactly low-rank) from its few noisy measurements b=A(X)+n with bounded constraint ‖n‖2≤ϵ, provided that tk-order restricted isometr...

This paper tackles the problem of H-infinity (H∞) norm computation for a commensurate Fractional Order System (FOS). First, H∞ norm definition is given for FOS and Hamiltonian matrix of a FOS is computed. Two methods based on this Hamiltonian matrix are then proposed to compute the FOS H∞ norm: one based on a dichotomy algorithm and another one on LMI conditions. The LMI conditions are based on...

We describe a novel approach to optimizing matrix problems involving nuclear norm regularization and apply it to the matrix completion problem. We combine methods from non-smooth and smooth optimization. At each step we use the proximal gradient to select an active subspace. We then find a smooth, convex relaxation of the smaller subspace problems and solve these using second order methods. We ...