In theoretical quantum computer science, understanding where and how computational speed-ups occur while applying quantum properties is a primary goal. In this paper, we study such problem under the framework of Quantum Query Model and prove the significance of L1-norm in the simulation of a given quantum algorithm. This result is presented by upper-bounds for the quotient between optimal class...

Let A be a complex m × n matrix. We find simple and good lower bounds for its spectral norm ‖A‖ = max{ ‖Ax‖ | x ∈ C, ‖x‖ = 1 } by choosing x smartly. Here ‖ · ‖ applied to a vector denotes the Euclidean norm.

Aiming to unify known results about clustering mixtures of distributions under separation conditions, Kumar and Kannan [KK10] introduced a deterministic condition for clustering datasets. They showed that this single deterministic condition encompasses many previously studied clustering assumptions. More specifically, their proximity condition requires that in the target k-clustering, the proje...

We study the class of polynomial threshold functions using harmonic analysis and apply the results to derive lower bounds related to ACo functions. A Boolean function is polynomial threshold if it can be represented as a sign function of a sparse polynomial (one that consists of a polynomial number of terms). Our main result is that the class of polynomial threshold functions can be characteriz...

In this paper we get the explicit condition number formulas for the W–weighted Drazin inverse of a rectangular matrix using the Schur decomposition and the spectral norm. We characterize the spectral norm and the Frobenius norm of the relative condition number of the W– weighted Drazin inverse, and the level-2 condition number of the W– weighted Drazin inverse. The sensitivity for the W–weighte...

This paper establishes the following results concerning the estimation of the power spectrum of a single, deterministic, infinitely long signal. a) If ŝx is the signal's power spectral density, correlogram spectral estimates obtained from increasingly longer signal segments tend to ŝx * ŵ/2π in the L-norm, where ŵ is the Fourier transform of the window used to generate the estimates. b) The L-n...