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node111.html
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<!DOCTYPE html>
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<html>
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<title>局部重新正交化和检测虚假的Ritz值</title>
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<h4><a name="SECTION001344030000000000000">
局部重新正交化和检测虚假的Ritz值</a>
</h4>
如果我们选择或被迫只能使用局部重正交化，
那么三对角矩阵 <span class="math-inline">T</span> 的一些特征值将是已经收敛特征值的新副本，
并且我们还会得到 <span class="math-inline">T</span> 的<i>伪</i>特征值。这样的特征值会突然出现在某个步骤 <span class="math-inline">j</span>，
仅在下一步骤消失。
<p>
卡勒姆(Cullum) [<a href="node421.html#cuwi81">90</a>] 设计了一种方法来剔除这些多余的副本和伪值。她取三对角矩阵 <span class="math-inline">T_j</span> 和另一个
<span class="math-inline">\hat{T}_2</span>，后者是通过删除 <span class="math-inline">T_j</span> 的第一行和第一列得到的。
所有非常接近 <span class="math-inline">\hat{T}_2</span> 特征值的 <span class="math-inline">T_j</span> 特征值需要特别考虑。
如果这样的特征值是 <span class="math-inline">T_j</span> 的多个特征值，保留其中一个，
其余的作为副本丢弃，记住未约化的三对角矩阵根据定义只有简单特征值。
如果 <span class="math-inline">T_j</span> 的简单特征值也是 <span class="math-inline">\hat{T}_2</span> 的特征值，它就是伪值，应该丢弃。
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<b>下一节：</b><a name="tex2html2425" href="node112.html">可用的软件</a>
<b>上一级：</b><a name="tex2html2419" href="node108.html">重新正交化</a>
<b>上一节：</b><a name="tex2html2415" href="node110.html">选择重新正交化</a>
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<address>
Susan Blackford
2000-11-20
</address>
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