The Solution of Least Squares Problems Using Krylov Subspace Methods

例如，当一个人想要找到方程比未知数多的线性方程组的解时，最小二乘问题就产生了。这样的问题出现在科学、工程和社会学中，例如，在统计学、调查和控制中，人们开发出一个最符合观测数据的模型方程。在这项研究中，我们开发了一种新的方法，利用迭代格式高效而准确地求解大型、困难的最小二乘问题。通过数值实验和理论验证了该方法的有效性。

Least squares problems arise, for instance, when one wants to find a solution to system of linear equations where there are more equations than unknowns. Such problems arise in science, engineering and sociology, for instance, in statistics, survey and control, where one develops a model equation which best fits observed data. In this research, we developed a new method to solve large and difficult least squares problems efficiently and accurately using an iterative scheme. We demonstrated the effectiveness of the method by numerical experiments and theory.