Related papers: Matrix Spectral Factorization for SA4 Multiwavelet
The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions…
In this paper, a method via sparse-sparse iteration for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix is proposed. The resulting factorized sparse approximate inverse is used as a…
The unpivoted and pivoted Householder QR factorizations are ubiquitous in numerical linear algebra. A difficulty with pivoted Householder QR is the communication bottleneck introduced by pivoting. In this paper we propose using random…
This paper is concerned with the inverse elastic scattering problem to determine the shape and location of an elastic cavity. By establishing a one-to-one correspondence between the Herglotz wave function and its kernel, we introduce the…
Matrix factorization-based recommender system is in effect an angle preserving dimensionality reduction technique. Since the frequency of items follows power-law distribution, most vectors in the original dimension of user feature vectors…
Matrix factorization is one of the best approaches for collaborative filtering, because of its high accuracy in presenting users and items latent factors. The main disadvantages of matrix factorization are its complexity, and being very…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…
Matrix factorization (MF) is a common method for collaborative filtering. MF represents user preferences and item attributes by latent factors. Despite that MF is a powerful method, it suffers from not be able to identifying strong…
This is the first article in a series of two dealing with a matrix approach for aberration quantification and correction in ultrasound imaging. Advanced synthetic beamforming relies on a double focusing operation at transmission and…
Multiresolution Matrix Factorization (MMF) was recently introduced as an alternative to the dominant low-rank paradigm in order to capture structure in matrices at multiple different scales. Using ideas from multiresolution analysis (MRA),…
Spectral factorization is a prominent tool with several important applications in various areas of applied science. Wiener and Masani proved the existence of matrix spectral factorization. Their theorem has been extended to the…
A scheme to encode arbitrarily long integer pairs on degenerate optical parametric oscillations multiplexed in time is proposed. The classical entanglement between the polarization directions and the phases of the oscillating pulses,…
We want to construct a homological link invariant whose Euler characteristic is MOY polynomial as Khovanov and Rozansky constructed a categorification of HOMFLY polynomial. The present paper gives the first step to construct a…
We obtain conditions for a trigonometric polynomial t of one variable to equal or be approximated by |p|^2 where p has frequencies in a Bohr set of integers obtained by projecting lattice points in the open planar region bounded by the…
Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric…
This paper studies the problem of multichannel spectral super-resolution with either constant amplitude (CA) or not. We propose two optimization problems based on low-rank Hankel-Toeplitz matrix factorization. The two problems effectively…
We study the problem of hyperparameter tuning in sparse matrix factorization under Bayesian framework. In the prior work, an analytical solution of sparse matrix factorization with Laplace prior was obtained by variational Bayes method…
The wavefunction for the multiparticle Schr\"odinger equation is a function of many variables and satisfies an antisymmetry condition, so it is natural to approximate it as a sum of Slater determinants. Many current methods do so, but they…
Matrix factorization is a key tool in data analysis; its applications include recommender systems, correlation analysis, signal processing, among others. Binary matrices are a particular case which has received significant attention for…
The resonant mode approximation of the scattering matrix is considered for calculating the optical properties of multilayered periodic structures within the formalism of the Fourier-modal method for two diffraction thresholds in close…