At 03:39 PM 5/20/2006, Fred lunnon wrote: Suppose instead we modify it to the more amenable

B := A; B := (B + B^{+T})/2 (average B with its transposed pseudo-inverse). For real nonsingular square A, the result appears to converge to an orthogonal matrix B such that A = B C with C symmetric: the "polar decomposition" of A. Presumably this must be well-known; but oddly it doesn't seem to be mentioned in in Higham et al ...

This iteration is well-known in the graphics community. I don't know whether it is covered in "Graphics Gems" or not. The graphics and robotics communities have been pushing certain areas of matix algebra (at least for small matrices -- up to 4x4, 5x5, etc.) really, really hard. The classic matrix math books don't seem to have kept up...