
104
U. von Matt
matrix U can then be obtained from the QR-decomposition (without pivoting) of
BV:
BV = UR.
Care must be taken that the diagonal elements of R remain nonnegative.
We get an alternative way of computing the left singular vectors by partitioning the
orthogonal matrix P in (1) into
n-by-n
submatrices:
[ Pll P12 ]
P= /~ /~ "
If B is nonsingular then we must have Pll = P22 = 0, and P12 is an orthogonal matrix
consisting of the left singular vectors of B. Even in the presence of rounding errors we can
force Pll and P22 to go to zero by an appropriate convergence criterion. ...