As the Givens' rotations are applied to the bidiagonal matrix, they are also applied to matrices in which the left and right singular vectors are accumulated (matrices $U$ and $V$). If we start with an $m \times m$ matrix, one step of introducing the bulge and chasing it out the matrix requires $O( m )$ computation. Accumulating the Givens' rotations into $U$ and $V$ requires $O( m^2 )$ computation for each such step, with $O( m^2 )$ data. As was discussed in Unit 10.4.4 for the implicitly shifted QR algorithm, this inherently means the cost of accessing data dominates on current architectures.