ABSTRACT
Then perhaps the most common way of determining x is to minimize ||r|| over x E R n , where the norm is some norm on R m . This involves an underlying assumption that A is exact, and all the errors are in 6, and this may not be the case in many practical situations. The effect of errors in A as well as b has been recognized and studied for many years, mainly in the statistics literature. One way to take the more general case into account is to solve the problem
minimize \\E : d\\ subject to (A + E)x = b + d, (1-1)
where the m atrix norm is one on (m x (n + 1)) matrices. This problem, when the m atrix norm is the Frobenius norm, was first analyzed by Golub and Van Loan [7], who used the term total least squares, and developed an algorithm based on the singular value decomposition of [A : b]. However, for problems for which A is nearly exact, this formulation may exaggerate the errors in A , and
