Editing QR algorithm (section)

=== Speeding up: Shifting and deflation ===
The slowdown when the ellipse gets more circular has a converse: It turns out that when the ellipse gets more stretched - and less circular - then the rotation of the ellipse becomes faster. Such a stretch can be induced when the matrix <math>M</math> which the ellipse represents gets replaced with <math>M-\lambda I</math> where <math>\lambda</math> is approximately the smallest eigenvalue of <math>M</math>. In this case, the ratio of the two semi-axes of the ellipse approaches <math>\infty</math>. In higher dimensions, shifting like this makes the length of the smallest semi-axis of an ellipsoid small relative to the other semi-axes, which speeds up convergence to the smallest eigenvalue, but does not speed up convergence to the other eigenvalues. This becomes useless when the smallest eigenvalue is fully determined, so the matrix must then be ''deflated'', which simply means removing its last row and column.

The issue with the unstable fixed point also needs to be addressed. The shifting heuristic is often designed to deal with this problem as well: Practical shifts are often discontinuous and randomised. Wilkinson's shift—which is well-suited for symmetric matrices like the ones we're visualising—is in particular discontinuous.