The spectral k-support norm enjoys good estimation properties in low rank matrix learning problems, empirically outperforming the trace norm. Its unit ball is the convex hull of rank k matrices with unit Frobenius norm. In this paper we generalize the norm to the spectral (k, p)support norm, whose additional parameter p can be used to tailor the norm to the decay of the spectrum of the underlyi...

We analyze the homothety types of associative bilinear forms that can occur on a Hopf algebra or on a local Frobenius k-algebra R with residue field k. If R is symmetric, then there exists a unique form on R up to homothety iff R is commutative. If R is Frobenius, then we introduce a norm based on the Nakayama automorphism of R. We show that if two forms on R are homothetic, then the norm of th...

In this paper, we present novel deterministic algorithms for multiplying two n× n matrices approximately. Given two matrices A,B we return a matrix C′ which is an approximation to C = AB. We consider the notion of approximate matrix multiplication in which the objective is to make the Frobenius norm of the error matrix C − C′ arbitrarily small. Our main contribution is to first reduce the matri...

We study the question of estimating the eigenvalues of a matrix in the streaming model, addressing a question posed in [Mut05]. We show that the eigenvalue “heavy hitters” of a matrix can be computed in a single pass. In particular, we show that the φ-heavy hitters (in the `1 or `2 norms) can be estimated in space proportional to 1/φ. Such a dependence on φ is optimal. We also show how the same...

1. Abstract This paper focuses on the use of minimum norm ellipsoids in stress-based fatigue criteria. We consider both the theoretical issues involved in constructing mathematical models for high cycle fatigue endurance limits and the computational features concerning the application of the resulting fatigue criteria. In the present approach, the macroscopic level of continuum is enhanced with...

In this paper, the effect of the impulse response of pulse shaping filters on a fractional sampling orthogonal frequency division multiplexing (FS OFDM) system is investigated. FS achieves path diversity with a single antenna through oversampling and subcarrier-based maximal ratio combining (MRC). Though the oversampling increases diversity order, correlation among noise components may deterior...

We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as much as possible relative to their distances in original data space. This approach can be considered as a deterministic Bi-Lipschitz embedding o...

A countable discrete group is said to be Frobenius stable if every function from the unitary matrices that “almost multiplicative” in norm “close” a representation norm. The purpose of this paper show finitely generated nilpotent groups are not virtually cyclic stable. Our argument proves same result for other unnormalized Schatten p-norms with 1<p≤∞.

Hybrid beamforming is a promising concept to achieve high data rate transmission at millimeter waves. To implement it in a transceiver, many references optimally adapt to a high-dimensional multi-antenna channel but more or less ignore the complexity of the channel estimation. Realizing that received coupling coefficients of the channel and pairs of possible analog beamforming vectors can be us...