Efficient Algorithms for Computing a Strong Rank-Revealing QR Factorization

Given an $m \times n$ matrix $M$ with $m \geqslant n$, it is shown that there exists a permutation $\Pi $ and an integer $k$ such that the QR factorization \[ M\Pi = Q\left( {\begin{array}{*{20}c} {A_k } & {B_k } \\ {} & {C_k } \\ \end{array} } \right) \] reveals the numerical rank of $M$: t...

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