February 1, 1987

The Smallest Perturbation of a Submatrix which Lowers the Rank and Constrained Total Least Squares Problems

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Abstract

Let \ T = [ array{*{20c} A & B \\ C & D \\ array } \] be a. partitioned rectangular matrix. We exhibit perturbations of D of smallest norm which lower the rank of T. We apply this result to generalize the total least squares problem Sx = b when only a rectangular subset of the data S, b is considered uncertain.

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James Demmel (Sun,) studied this question.

synapsesocial.com/papers/6a1ea595004237b903a40bc8 https://doi.org/https://doi.org/10.1137/0724016

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