We consider stable signal recovery in `q quasi-norm for 0 < q ≤ 1. In this problem, given a measurement vector y = Ax for some unknown signal vector x ∈ R and a known matrix A ∈ Rm×n, we want to recover z ∈ R with ‖x − z‖q = O(‖x − x‖q) from a measurement vector, where x∗ is the s-sparse vector closest to x in `q quasi-norm. Although a small value of q is favorable for measuring the distance to...

The appropriateness of Zinterhof sequences to be used in GRID-based QMC integration is discussed. Theoretical considerations as well as experimental investigations are conducted comparing and assessing different strategies for an efficient and reliable usage. The high robustness and ease of construction exhibited by those sequences qualifies them as excellent QMC point set candidates for hetero...

In this paper, we present a parallel quasi-Chebyshev acceleration applied to the nonoverlapping multisplitting iterative method for the linear systems when the coefficient matrix is either an H-matrix or a symmetric positive definite matrix. First, m parallel iterations are implemented in m different processors. Second, based on l1-norm or l2-norm, the m optimization models are parallelly treat...

Abstract We provide a characterization of the Radon–Nikodým property for Banach space Y in terms denseness bounded linear operators into which attain their norm weak sense, complement one given by Bourgain and Huff 1970s domain spaces. To this end, we introduce following notion: an operator $$T:X \longrightarrow Y$$ T</m...

This paper proposes an Lp (0&#x003C;p&#x003C;1) quasi norm state estimator for power system static estimation. Compared with the existing L, and L2 estimators, proposed can suppress bad data more effectively. The robustness of is discussed, analysis shows that its ability to increases as $p$ decreases. Moreover, algorithm suggested solve non-convex estimation pr...

to obtain an approximate second-order KKT solution of the `p-norm models in polynomial time with a fixed error tolerance, and then test our `p-norm models on CRSP(1992-2013) and also S&P 500 (2008-2012) data. The empirical results illustrate that our `p-norm regularized models can generate portfolios of any desired sparsity with portfolio variance, portfolio return and Sharpe Ratio comparable t...

We construct a quasi-Banach space which cannot be given an equivalent plurisubharmonic quasi-norm, but such that it has a quotient by a onedimensional space which is a Banach space. We then use this example to construct a compact convex set in a quasi-Banach space which cannot be atfinely embedded into the space L0 of all measurable functions.