Editing Open Problems:12
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− | {{ | + | {{DISPLAYTITLE:Problem 12: Deterministic $CUR$-Type Decompositions}} |
− | | | + | {{Infobox |
− | | | + | |label1 = Proposed by |
+ | |data1 = Michael Mahoney | ||
+ | |label2 = Source | ||
+ | |data2 = [[Workshops:Kanpur_2006|Kanpur 2006]] | ||
+ | |label3 = Short link | ||
+ | |data3 = http://sublinear.info/12 | ||
}} | }} | ||
A $CUR$-decomposition of $A$ expresses $A$ as a product of three | A $CUR$-decomposition of $A$ expresses $A$ as a product of three | ||
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original data. Note the structural simplicity of a CUR matrix | original data. Note the structural simplicity of a CUR matrix | ||
decomposition: | decomposition: | ||
− | + | \begin{equation*} | |
\underbrace{\left( | \underbrace{\left( | ||
\begin{array}{ccccc} | \begin{array}{ccccc} | ||
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\begin{array}{ccccc} &&&& \\ &&R&& \\ &&&& \end{array} | \begin{array}{ccccc} &&&& \\ &&R&& \\ &&&& \end{array} | ||
\right)}_{r \times n} . | \right)}_{r \times n} . | ||
− | + | \end{equation*} | |
We briefly expand on the latter point. In many cases, an important | We briefly expand on the latter point. In many cases, an important |