奇异矩阵的Krylov方法的误差分析比较

Error Analysis of Krylov Method of Singular Matrix

Krylov方法是求解线性方程组Ax=b,A∈CN×N,b∈CN的一种迭代方法,当A非奇异时,已有很好研究.而当A奇异或接近奇异阵时,在一定的假定条件下,Krylov方法的解与范教最小的最小二乘解A+b之间的差是可以估计出来的.

Krylov subspace method is an iteration method of solving the linear equation Ax=b,A∈CN×N,b∈CN. When the matrix A is nonsigular,it is wellunderstooded. But when A is or near to singular,Krylov method may cannot get the solution (or leastsquare solution),under some assumption,the error between solution of Krylov method and the leastsquare solution can be estimated.