Lower dimensional representation of text data in vector space based information retrieval
Computational information retrieval
Trail to a Lyapunov equation solver
Computers & Mathematics with Applications
Additive preconditioning and aggregation in matrix computations
Computers & Mathematics with Applications
Efficient construction of a reduced system in multi-domain system with free subdomains
Finite Elements in Analysis and Design
Nonnegative rank factorization--a heuristic approach via rank reduction
Numerical Algorithms
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Matrix factorization in numerical linear algebra (NLA) typically serves the purpose of restating some given problem in such a way that it can be solved more readily; for example, one major application is in the solution of a linear system of equations. In contrast, within applied statistics/psychometrics (AS/P), a much more common use for matrix factorization is in presenting, possibly spatially, the structure that may be inherent in a given data matrix obtained on a collection of objects observed over a set of variables. The actual components of a factorization are now of prime importance and not just as a mechanism for solving another problem. We review some connections between NLA and AS/P and their respective concerns with matrix factorization and the subsequent rank reduction of a matrix. We note in particular that several results available for many decades in AS/P were more recently (re)discovered in the NLA literature. Two other distinctions between NLA and AS/P are also discussed briefly: how a generalized singular value decomposition might be defined, and the differing uses for the (newer) methods of optimization based on cyclic or iterative projections.