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The classical low rank approximation problem is to find a rank $k$ matrix $UV$ (where $U$ has $k$ columns and $V$ has $k$ rows) that minimizes the Frobenius norm of $A - UV$.
A weighted-least-squares matrix decomposition method with applications to the design of two-dimensional digital filters
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On the computational complexity and geometry of the first-order theory of the reals. part i: Introduction. preliminaries. the geometry of semi-algebraic sets. the decision problem for the existential theory of the reals
James Renegar · 1992
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On the computational complexity and geometry of the first-order theory of the reals. part ii: The general decision problem. preliminaries for quantifier elimination
James Renegar · 1992
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On the combinatorial and algebraic complexity of quantifier elimination
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Weighted low-rank approximation of general complex matrices and its application in the design of 2-d digital filters
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New method for weighted low-rank approximation of complex-valued matrices and its application for the design of 2-d digital filters
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Weighted low rank approximations with provable guarantees
Ilya P. Razenshteyn, Zhao Song, and David P. Woodruff · 2016
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Haim Avron, Kenneth L. Clarkson, and David P. Woodruff · 2017
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Practical sketching algorithms for low-rank matrix approximation
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Mert Pilanci and Martin J Wainwright · 2015
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