Discrete matrix Schrodinger equation equivalents of discrete two-component matrix wave systems

Discrete Trigonometric Matrix Functions

We explore a pair of matrix solutions to a certain discrete system which has various properties similar to the familiar continuous trigonometric functions, including basic identities and sum and difference of two angles formulas. Then we examine separation properties of these matrices. An oscillation result is also given.

Optimal Discrete Matrix Completion

In recent years, matrix completion methods have been successfully applied to solve recommender system applications. Most of them focus on the matrix completion problem in real number domain, and produce continuous prediction values. However, these methods are not appropriate in some occasions where the entries of matrix are discrete values, such as movie ratings prediction, social network relat...

Robust Discrete Matrix Completion

Most existing matrix completion methods seek the matrix global structure in the real number domain and produce predictions that are inappropriate for applications retaining discrete structure, where an additional step is required to post-process prediction results with either heuristic threshold parameters or complicated mappings. Such an ad-hoc process is inefficient and impractical. In this p...

Discrete-time Equivalents to Continuous-time Systems

Inverse scattering transform for the integrable discrete nonlinear Schrodinger equation

The inverse scattering transform for an integrable discretization of the defocusing nonlinear Schrodinger equation with nonvanishing boundary values at infinity is constructed. This problem had been previously studied, and many key results had been established. Here, a suitable transformation of the scattering problem is introduced in order to address the open issue of analyticity of eigenfunct...