Lawson and Hanson (1995) proved that the problem (11) is equivalent to the least-squares problem
If the primal problem (19) has an unbounded optimal solution, then the least-squares problem (23) has for every [z.
If the LP problem is degenerate, ill-conditioned or we have any initial basis, then it is expedient to start the solution process with the least-squares problem (23).
Definition 3: The Structured Total Least-Squares problem
seeks to minimize the error vector [e.
2] as bound-constrained linear least-squares problems by ADM.
CHAN, A reduced Newton method for constrained linear least-squares problems, J.
We now have a true least-squares problem, which again can be solved with the SVD.
4) is equal to the smallest singular value and thus minimal, and we have solved the linearized least-squares problem.
To achieve this, our strategy in cases with [tau] [greater than or equal to] 2 is to reduce the denominator degree from n to n - ([tau] - 1) and start the approximation process again, now inevitably as a least-squares problem rather than interpolation since N is unchanged (line 42).
Also, rank revealing factorization can be used to solve least-squares problems
using the method proposed by Bjorck [1, 2].
1) This is a formal derivation and it is worth noting that one should not form generalized inverses as a method for computing solutions to linear least-squares problems
The efficient algorithms developed in this work were used to solve large-scale least-squares problems
involving millions of observations from the National Geodetic Survey.