Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general solution of a singular system is of a bounded sensitivity as a unique element in an affine Grassmannian. If a singular linear system is given through empirical data that are sufficiently accurate with a tight error bound, a properly formulated general numerical solution uniquely exists in the same affine Grassmannian, enjoys Lipschitz continuity and approximates the underlying exact solution with an accuracy in the same order as the data. Furthermore, any backward accurate numerical solution vector is an accurate approximation to one of the solutions of the underlying singular system.

翻译：解决单个矢量溶液的单线性系统是一个存在条件编号无限性的错误问题。 然而,从另一个角度看,单项系统的一般解决办法是作为草根法中一个独特元素的封闭敏感度。如果单项线性系统是通过经验数据提供的,而实验数据足够准确,并带有严格的误差,那么,一个设计得当的通用数字解决方案就存在于同一个松树法中,具有利普西茨连续性,并按与数据相同的顺序以精确度接近基本的确切解决方案。此外,任何后向精确的数字解决方案矢量都是与基本单项系统的一种解决方案的准确近似值。