Preorderings, monotone functions, and best rank r approximations with applications to classical MDS

Authors

R. Mathar, R. Meyer,

Abstract

        This paper extends the classical results of Eckart and Young (1936) and Mirsky (1960) concerning the best rank r matrix approximation with respect to certain preorderings defined on the space of complex n*k matrices. A note on some related work of Jensen (1991) is included, his assertions, though, are shown to be flawed. In a second part we turn to the problem of approximating a Hermitian matrix by a positive semidefinite matrix of given rank which is of major relevance in the context of multidimensional scaling (MDS). Further universally optimal properties of the classical MDS solution are provided.

BibTEX Reference Entry 

@article{MaMe93,
	author = {Rudolf Mathar and Renate Meyer},
	title = "Preorderings, monotone functions, and best rank r approximations with applications to classical {MDS}",
	pages = "291-305",
	journal = "Journal of Statistical Planning and Inference",
	volume = "37",
	year = 1993,
	}

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