Condition Number Estimation Of The Linear Least Squares Problem Based On The Conjugate Method

In numerical analysis condition numbers describe the sensitivity of the solution of the problem regarding on the input data perturbation,which is also a major research topic in matrix analysis.Many classical results had been obtained during past years in matrix computation, such as the problem of solving linear system.In this thesis we will focus on the conditioning of the linear least squares problems: (?)There are three parts in this thesis. In the fist part, we will briefly introduce some theoretical knowledge, including classical condition number theory, linear least squares problems and some pervious results on normwise and componentwise condition numbers. We will introduce the small sample condition estimation method in the second part. At last, we will adopt the conjugate method and derive the conditioning estimation for the least squares problems. According to the numerical experiments, the estimation method is fast and efficient.