矩阵特征值和特征向量计算.ppt

《矩阵特征值和特征向量计算.ppt》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、第九章.矩阵特征值和特征向量计算但高次多项式求根精度低,一般不作为求解方法.目前的方法是针对矩阵不同的特点给出不同的有效方法.工程实践中有多种振动问题，如桥梁或建筑物的振动，机械机件、飞机机翼的振动，及一些稳定性分析和相关分析可转化为求矩阵特征值与特征向量的问题。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.§1.幂法和反幂法.一、幂法求矩阵的按模最大的特征值与相应的特征向量。它是通过迭代产生

2、向量序列，由此计算特征值和特征向量。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientP

3、rofile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAsp

4、ose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.两种特殊情况Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePty

5、Ltd.幂法小结Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.二、幂法的加速因为幂法的收敛速度是线性的，而且依赖于比值，当比值接近于1时，幂法收敛很慢。幂法加速有多种，介绍两种。Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluati

6、ononly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright200

7、4-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.Evaluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.Copyright2004-2011AsposePtyLtd.三、反幂法反幂法是计算矩阵按模最小的特征值及特征向量的方法，也是修正特征值、求相应特征向量的最有效的方法。Ev

8、aluationonly.CreatedwithAspose.Slidesfor.NET3.5ClientProfile5.2.0.0.