In this paper, we first get further consideration of the order perturbation with normwise condition number MTLS problem. For easy estimation, show a lower bound for which is proved to be optimal. overcome problems encountered in calculating number, give an upper computing more effectively and nonstandard unusual bounds Both two types can enjoy storage computational advantages. getting insight i...

A fundamental task in scientific computing is to estimate parameters in a mathematical model from collected data which are subject to errors. The influence of the errors can be reduced by using a greater number of data than the number of unknowns. If the model is linear, the resulting problem is then to “solve” an in general inconsistent linear system Ax = b, where A ∈ Rm×n and m ≥ n. In other ...

Here we solve linear systems Ax = b that do not have a solution. If b is not in the column space of A, there is no x such that Ax = b. The best we can do is to find a vector y that brings left and right hand side of the linear system as close as possible, in other words y is chosen to make the distance between Ay and b as small as possible. That is, we want to minimize the distance ‖Ax − b‖2 ov...