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The aim of Non-negative Matrix Factorization (NMF) is to decompose a non-negative matrix into a product of two (or multiple) non-negative matrices with reduced ranks. Several iterative methods have been developed for this purpose, e.g. the Alternating Least Squares (ALS) or Lee-Seung (LS) multiplicative methods. Despite its fast convergence, the ALS algorithm suffers from its instability, and may...
We prove a convergence result and a data dependence for Ishikawa iteration when applied to contraction-like operators. An example is given, in which instead of computing the fixed point of an operator, we approximate the operator with a contractive-like one. For which it is possible to compute the fixed point, and therefore to approximate the fixed point of the initial operator.
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