Abstract
The decomposition of a matrix, as a product of factors with particular properties, is a much used tool in numerical analysis. Here we develop methods for decomposing a matrix C into a product XY, where the factors X and Y are required to minimize their distance from an arbitrary pair $$X_0$$X0 and $$Y_0$$Y0. This type of decomposition, a projection to a matrix product constraint, in combination with projections that impose structural properties on X and Y, forms the basis of a general method of decomposing a matrix into factors with specified properties. Results are presented for the application of these methods to a number of hard problems in exact factorization.
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