On 5/20/06, Fred lunnon <fred.lunnon@gmail.com> 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 ...
Ah yes, it is --- (3.6) on page 6 of JA's 3rd reference: \jjbibitem{matrixsign}{Nicholas J.\ Higham: \jjbibtitle{The Matrix Sign Decomposition and its Relation to the Polar Decomposition}, Linear Algebra and Appl., 212/213, pp.3-20, 1994. Online at \url{http://citeseer.ist.psu.edu/higham94matrix.html}.} WFL