线性方程组迭代方法残差光滑技术的一个推广

1　引　　言我们考虑求解线性方程组Ax=b,A∈Rn×n,b,x∈Rn.(1)的迭代方法.迭代序列{xk}的性态常常由与之对应的残差范数序列{‖rk‖}的特性来决定.人们自然希望{‖rk‖}光滑地(单调地)收敛到0.在所有Krylov子空间方法中,GMRES7]方法因为可使{‖rk‖}最优地趋于0,故是一个较为成功的方法.但是,GMRES方法的工作量和存贮量却随着迭代步数的增加而迅速增加.而BCG4]和CGS10]等方法具有运算量小,收敛快等突出优点.但它们的残差范数性态却很不规则,{‖rk‖}振荡不定.这给判断收敛性及何时停机带来很大的不便.残差光滑技术是一个行之有…

A GENERALIZATION OF RESIDUAL SMOOTHING TECHNIQUE FOR ITERATIVE METHODS

The residual norm behavior of an iterative method for solving linear systems Ax=b is of particular importance. Residual smoothing technique is named for the strategy that improve the residual norm behavior simply via a two term weighted mean of some two points (iterates). A generalization from the two point residual smoothing technique to m point residual smoothing, which is obtained by a m term weighted mean of some m points, is studied and explored. A new hybrid iterative method combining this generalization with restarting approach is presented. Results of numerical experiments comparing the generalization with the original residual smoothing are reported.