My paper describing the connection between the Householder decomposition of and the canonical coset parametrization of unitary operators was published today in the Journal of Mathematical Physics
J. Math. Phys. 51, 082101 (2010)
This parametrization is very useful for calculating the parameters that uniquely characterises a given unitary operator U(N). I show that instead of solving a complicated systems of non-linear equations one can perform very stable and efficient Householder transformations. Right now I am working on some practical applications based on that result.