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- Moody T. Chu, Matthew M. Lin
- SIAM J. Scientific Computing
- 2008

In this study, nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets. Working on the probability simplex has the advantage that data are limited to a compact set with known boundary, making it easier to trace the approximation procedure. In particular, the… (More)

- Matthew M. Lin, Bo Dong, Moody T. Chu
- Numerical Algorithms
- 2009

In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or… (More)

Abstract. Any given nonnegative matrix A ∈ R can be expressed as the product A = UV for some nonnegative matrices U ∈ R and V ∈ R with k ≤ min{m, n}. The smallest k that makes this factorization possible is called the nonnegative rank of A. Computing the exact nonnegative rank and the corresponding factorization are known to be NP-hard. Even if the… (More)

- Matthew M Lin, Moody T Chu
- Linear algebra and its applications
- 2010

The Euclidean distance matrix for n distinct points in ℝ (r) is generically of rank r + 2. It is shown in this paper via a geometric argument that its nonnegative rank for the case r = 1 is generically n.

Matrix factorization has been of fundamental importance in modern sciences and technology. This work investigates the notion of factorization with entries restricted to integers or binaries, , where the “integer” could be either the regular ordinal integers or just some nominal labels. Being discrete in nature, such a factorization or approximation cannot… (More)

- Bo Dong, Matthew M Lin, Moody T Chu
- Journal of sound and vibration
- 2009

Quadratic matrix polynomials are fundamental to vibration analysis. Because of the predetermined interconnectivity among the constituent elements and the mandatory nonnegativity of the physical parameters, most given vibration systems will impose some inherent structure on the coefficients of the corresponding quadratic matrix polynomials. In the inverse… (More)

- Zhi Zhao, Xiao-Qing Jin, Matthew M. Lin
- J. Comput. Physics
- 2016

- Matthew M. Lin
- SIAM J. Matrix Analysis Applications
- 2011

Modern economic theory views the economy as a dynamical system in which rational decisions are made in the face of uncertainties. The dynamics includes changes over time of market behavior such as consumption, investment, labor supply, and technology innovation, all interpreted in a broad sense. The Euler equation arises as the first order optimality… (More)

- Matthew M. Lin
- Applied Mathematics and Computation
- 2015