Some ill-conditioned processes are very sensitive to small elementwise
uncertainties arising in classical element-by-element model identific
ations. For such processes, accurate identification of singular values
and right singular vectors are more important than those of the eleme
nts themselves. Singular values and right singular vectors can be foun
d by iterative identification methods that implement the input and out
put transformations iteratively. Methods based on SVD decomposition, Q
R decomposition, and LU decomposition are proposed and compared with K
uong and MacGregor's method. Convergence proofs are given. These SVD a
nd QR methods use orthogonal matrices for the transformations that can
not be calculated analytically in general, and so they are hard to app
ly to dynamic processes, whereas the LU method uses simple analytic tr
ansformations and can be directly applied to dynamic processes.