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<title>Medline SVD结果</title>
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<h4><a name="SECTION001346020000000000000">
Medline SVD 结果</a>
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第二个测试例子 Medline SVD 表现得相当不同。主要的特征值（<span class="math-inline">\lambda_i(A)=\sigma_i(X)^2</span>）分离得相当好（最大的一个是 <span class="math-inline">\lambda_1=3442.5</span>，接下来一个是 <span class="math-inline">\lambda_2=756.6</span>），即使对于较大的 <span class="math-inline">i</span>，比值 <span class="math-inline">\lambda_i/\lambda_{i+1}</span> 较小，如图 <a href="node114.html#MedlLanRes">4.3</a> 所示，我们仍将获得快速的收敛。第一个特征值在第 <span class="math-inline">j=14</span> 步时已经达到了完全的精度，而在第 <span class="math-inline">j=50</span> 步后，前六个特征值已经收敛。在第 <span class="math-inline">j=300</span> 步后，我们得到了 100 个特征值。
<p>
<div style="text-align: center;">
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<img src="icon/MedlineRes.png" alt="图4.3：Medline SVD矩阵的残差估计。" id="MedlineRes"/>
<figcaption>图4.3：Medline SVD矩阵的残差估计。</figcaption>
</div>
<p>
这个分离良好的问题与 L 形膜问题之间还有一个有趣的差异，后者具有更多聚集的特征值，即重新正交化触发的频率更高。我们在第 <span class="math-inline">j=7</span> 步用一条虚线标记重新正交化，第 <span class="math-inline">j=12</span> 步又有一条，之后每四步标记一次。由于每次重新正交化涉及两个向量，选择性重新正交化所需的工作量大约是全面重新正交化的一半。在这种情况下，建议用户使用全面重新正交化，因为它能在算术工作量适度增加的情况下确保基向量的完全正交性。
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<address>
Susan Blackford
2000-11-20
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