= Randomized range finder
{title2=$Y=AX,\quad \widehat A=QQ^TA$}
Choose a random sampling <matrix> $X$, form $Y=AX$, and find an <orthonormal basis> $Q$ for the sampled <column space> by a thin <QR decomposition>. The <low-rank approximation> $\widehat A=QQ^TA$ keeps the component of $A$ in that space. Since $QQ^TAX=AX$, it reproduces the sampled action exactly. If $Y$ has deficient <matrix rank>, one can use only a <basis> of its <column space>; alternatively an <orthonormal> completion must be specified.
Back to article page
