Pillai "Ax= b, Least Squares (LS) & Total Least Squares (TLS)" скачать в хорошем качестве

Pillai "Ax= b, Least Squares (LS) & Total Least Squares (TLS)"

Classic problem of solving a set of linear equations of the form Ax=b is discussed here. These equations may be over determined(more equations than unknowns) or under determined (Less equations than unknowns), and/or can be consistent or not consistent. among themselves. The least square (LS) solution assumes the error to be in the observation vector b, and finds an x_0 vector such that Ax_0 = b_0 and the error in | b-b_0 |^2 is minimized. The singular value decomposition (SVD) of the matrix A can be used to get the desired solution. In total least squares (TLS), the error is assumed to be in both the model matrix A and the observation vector b, and the SVD of the extended matrix [A,b] is used in that case to find the desired solution x_1.