Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

Abstract: The frequency estimation of the harmonics in multiplicative and additive noise is investigated in this paper. To improve the frequency resolution of estimation, this paper proposes a SVD-based ESPRIT algorithm to estimate the frequency of harmonics in multiplicative and additive noise. The proposed SVD-based ESPRIT algorithm not only has high-resolution, but also is easy to be impleme...

There are two major formulations of image alignment using gradient descent. The first estimates an additive increment to the parameters (the additive approach), the second an incremental warp (the compositional approach). We first prove that these two formulations are equivalent. A very efficient algorithm was recently proposed by Hager and Belhumeur using the additive approach that unfortunate...

We explore additive models that combine both parametric and nonparamet-ric terms and propose a p n-consistent backktting estimator for the parametric component of the model. The theoretical properties of the estimator are developed for the case with a single nonparametric term and extended to an arbitrary number of nonparametric additive terms. An estimator for the optimal band-width making min...