四川师范大学学报(自然科学版)
四川師範大學學報(自然科學版)
사천사범대학학보(자연과학판)
JOURNAL OF SICHUAN NORMAL UNIVERSITY(Natural Science)
2010年
1期
42-44
,共3页
线性方程组%行处理迭代法%加速因子%动态加速
線性方程組%行處理迭代法%加速因子%動態加速
선성방정조%행처리질대법%가속인자%동태가속
system of linear equation%row action iteration method%accelerated factor%dynamic accelerated
在带加速因子的线性方程组通用性迭代解法的基础上,用几何方法对加速因子进行了讨论,证明了每次迭代中最佳加速因子的存在性,讨论了在每次迭代中使算法收敛的加速因子的取值范围,设计了一个动态调整加速因子的通用性迭代算法,并进行了程序验证.
在帶加速因子的線性方程組通用性迭代解法的基礎上,用幾何方法對加速因子進行瞭討論,證明瞭每次迭代中最佳加速因子的存在性,討論瞭在每次迭代中使算法收斂的加速因子的取值範圍,設計瞭一箇動態調整加速因子的通用性迭代算法,併進行瞭程序驗證.
재대가속인자적선성방정조통용성질대해법적기출상,용궤하방법대가속인자진행료토론,증명료매차질대중최가가속인자적존재성,토론료재매차질대중사산법수렴적가속인자적취치범위,설계료일개동태조정가속인자적통용성질대산법,병진행료정서험증.
Based on general iteration method with accelerated factor for linear equations, the accelerated factor is discussed by using geometrical method. It is proved that the best accelerated factor of every iteration is existent. Moreover the accelerated factor range in which the iteration is convergent is also discussed. Finaly, a general iteration method with dynamic adjusting accelerated factor is designed and checked.
