In this paper, we revisit the Computational Square-Root Exponent Problem (CSREP), and give a more generic condition such that CSREP is polynomial-time equivalent to the Computational DiffieHellman Problem (CDHP) in the group with prime order. The results obtained in this paper contain Zhang et al.’s results at IWCC2011. We also analyze the existence of such condition. Although primes satisfying...

The statistical analysis of covariance matrix data is considered, and in particular methodology is discussed which takes into account the non-Euclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix, and in particular ...

The statistical analysis of covariance matrix data is considered and, in particular, methodology is discussed which takes into account the nonEuclidean nature of the space of positive semi-definite symmetric matrices. The main motivation for the work is the analysis of diffusion tensors in medical image analysis. The primary focus is on estimation of a mean covariance matrix and, in particular,...

We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as a subspace fitting problem and analyze the difference between the solution su...

Hain and Freire have proposed different floating point square root algorithms that can be efficiently implemented in hardware. The algorithms are compared and evaluated on both performance and precision.

We present an r-th root extraction algorithm over a finite field Fq. Our algorithm precomputes a primitive r-th root of unity ξ where s is the largest positive integer satisfying r|q − 1, and is applicable for the cases when s is small. The proposed algorithm requires one exponentiation for the r-th root computation and is favorably compared to the existing algorithms.

A novel Fast RLS Algorithm based on the Givens Rotation and developed from an UDU T square-root fac-torization of autocorrelation matrix is discussed. The algorithm presents excellent numerical properties and requires 14N multiplications and 6N divisions per sampling interval, where N is the linear lter order.

Global covariance pooling in convolutional neural networks has achieved impressive improvement over the classical first-order pooling. Recent works have shown matrix square root normalization plays a central role in achieving state-of-the-art performance. However, existing methods depend heavily on eigendecomposition (EIG) or singular value decomposition (SVD), suffering from inefficient traini...