Related papers: Matrix Spectral Factorization for SA4 Multiwavelet
The computation of a matrix function $f(A)$ is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential equations. In this work, we use only matrix-vector products…
In this paper, we present a thorough investigation for a spontaneous parametric four-wave mixing process in third-order nonlinear waveguides with various continuous tapering patterns. It has been previously shown that these devices can…
In this paper, we provide novel algorithms with identifiability guarantees for simplex-structured matrix factorization (SSMF), a generalization of nonnegative matrix factorization. Current state-of-the-art algorithms that provide…
Sparse coding--that is, modelling data vectors as sparse linear combinations of basis elements--is widely used in machine learning, neuroscience, signal processing, and statistics. This paper focuses on the large-scale matrix factorization…
We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.
Here we discuss a regularized version of the factorization method for positive operators acting on a Hilbert Space. The factorization method is a qualitative reconstruction method that has been used to solve many inverse shape problems. In…
Recent studies have revealed that multi-soliton solutions of the nonlinear Schr\"odinger equation, as carriers of information, offer a promising solution to the problem of nonlinear signal distortions in fiber optic channels. In any…
We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…
This paper presents a product to sum approach for a fast and efficient matrix filling in a hierarchical finite-element method (FEM). Due to the existence of a coupling factor arising from the material and Jacobian inhomogeneities in curved…
The application of wavelet transforms to Synthetic Aperture Radar (SAR) imagery has improved despeckling performance. To deduce the problem of filtering the multiplicative noise to the case of an additive noise, the wavelet decomposition is…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
This paper investigates the inverse source problem with a single propagating mode at multiple frequencies in an acoustic waveguide. The goal is to provide both theoretical justifications and efficient algorithms for imaging extended sources…
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…
We present a generic scheme to construct corrected trapezoidal rules with spectral accuracy for integral operators with weakly singular kernels in arbitrary dimensions. We assume that the kernel factorization of the form,…
Factorial Schur functions are generalizations of Schur functions that have, in addition to the usual variables, a second family of "shift" parameters. We show that a factorial Schur function times a deformation of the Weyl denominator may…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses standard arithmetic, BMF uses the Boolean OR and Boolean AND…
Randomized sampling has recently been demonstrated to be an efficient technique for computing approximate low-rank factorizations of matrices for which fast methods for computing matrix vector products are available. This paper describes an…
Positive-definite matrices materialize as state transition matrices of linear time-invariant gradient flows, and the composition of such materializes as the state transition after successive steps where the driving potential is suitably…