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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6268ca104f8811599e18655b/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">班级：自动化<span class="_ _0"> </span><span class="ff2">1501 </span>姓名：付力<span class="ff2"> </span>学号：<span class="ff2">2015307201308</span></div><div class="t m0 x2 h4 y3 ff1 fs1 fc0 sc0 ls0 ws0">实验一<span class="ff2"> </span>误差分析</div><div class="t m0 x3 h5 y4 ff1 fs2 fc0 sc1 ls0 ws0">实验目的<span class="ff2 sc0"> </span></div><div class="t m0 x3 h3 y5 ff2 fs0 fc0 sc0 ls0 ws0"> <span class="ff1">了解误差在数值计算中的累积与传播，理解算法稳定性的重要性。</span></div><div class="t m0 x3 h5 y6 ff1 fs2 fc0 sc1 ls0 ws0">实验内容<span class="ff2 sc0"> </span></div><div class="t m0 x3 h3 y7 ff1 fs0 fc0 sc0 ls0 ws0">实验<span class="_ _0"> </span><span class="ff2">1</span></div><div class="t m0 x4 h6 y8 ff1 fs3 fc0 sc0 ls0 ws0">两个<span class="ff2"> Matlab<span class="_ _0"> </span></span>函数：“<span class="ff2">ro<span class="_ _1"></span>ots<span class="ff3">”<span class="ff1">和“</span></span>poly<span class="ff3">”<span class="ff1">，输入函数</span></span></span></div><div class="t m0 x5 h6 y9 ff2 fs3 fc0 sc0 ls0 ws0">u<span class="ff1">＝</span>roots<span class="ff1">（</span>a<span class="ff1">）</span></div><div class="t m0 x3 h6 ya ff1 fs3 fc0 sc0 ls0 ws0">其中若<span class="_ _2"></span>变量<span class="_ _3"> </span>存储<span class="_ _4"> </span>维的向<span class="_ _2"></span>量，则<span class="_ _2"></span>该函数<span class="_ _2"></span>的输出<span class="_ _3"> </span>为一个<span class="_ _3"> </span>维的向量。<span class="_ _2"></span>设<span class="_ _0"> </span><span class="ff2">a<span class="_ _5"> </span></span>的元素<span class="_ _2"></span>依</div><div class="t m0 x3 h6 yb ff1 fs3 fc0 sc0 ls0 ws0">次为<span class="_ _6"> </span>，则输出<span class="_ _5"> </span><span class="ff2">u<span class="_ _5"> </span></span>的各分量是多项式方程</div><div class="t m0 x3 h6 yc ff1 fs3 fc0 sc0 ls0 ws0">的全部根，而函数</div><div class="t m0 x6 h7 yd ff2 fs3 fc0 sc0 ls0 ws0">b=poly(v)</div><div class="t m0 x3 h6 ye ff1 fs3 fc0 sc0 ls0 ws0">的<span class="_ _7"></span>输<span class="_ _7"></span>出<span class="_ _8"> </span><span class="ff2">b<span class="_"> </span></span>是<span class="_ _7"></span>一<span class="_ _7"></span>个<span class="_ _8"> </span><span class="ff2">n<span class="_ _7"></span></span>＋<span class="_ _7"></span><span class="ff2">1<span class="_"> </span></span>维<span class="_ _7"></span>变<span class="_ _7"></span>量<span class="_ _7"></span>，<span class="_ _7"></span>它<span class="_ _2"></span>是<span class="_ _7"></span>以<span class="_ _9"> </span><span class="ff2">n<span class="_"> </span></span>维<span class="_ _7"></span>变<span class="_ _7"></span>量<span class="_ _8"> </span><span class="ff2">v<span class="_ _8"> </span></span>的<span class="_ _7"></span>各<span class="_ _7"></span>分<span class="_ _7"></span>量<span class="_ _7"></span>为<span class="_ _2"></span>根<span class="_ _7"></span>的<span class="_ _7"></span>多<span class="_ _7"></span>项<span class="_ _7"></span>式<span class="_ _7"></span>的<span class="_ _7"></span>系<span class="_ _7"></span>数<span class="_ _2"></span>。<span class="_ _7"></span>可<span class="_ _7"></span>见</div><div class="t m0 x3 h6 yf ff1 fs3 fc0 sc0 ls0 ws0">“<span class="ff2">roots<span class="ff3">”</span></span>和“<span class="ff2">Poly<span class="ff3">”</span></span>是两个互逆的运算函数<span class="ff2">.</span></div><div class="t m0 x4 h7 y10 ff2 fs3 fc0 sc0 ls0 ws0"> ve=zeros(1,21);</div><div class="t m0 x4 h7 y11 ff2 fs3 fc0 sc0 ls0 ws0"> ve(2)=ess;</div><div class="t m0 x4 h7 y12 ff2 fs3 fc0 sc0 ls0 ws0"> roots(poly(1:20))+ve)</div><div class="t m0 x4 h6 y13 ff1 fs3 fc0 sc0 ls0 ws0">上述简单的<span class="_ _5"> </span><span class="ff2">Matlab<span class="_ _5"> </span></span>程序便得到（<span class="ff2">1.2</span>）的全部根，程序中的“<span class="ff2">ess<span class="ff3">”</span></span>即是（<span class="ff2">1.2</span>）中的<span class="_ _a"> </span>。</div><div class="t m0 x3 h3 y14 ff1 fs0 fc0 sc0 ls0 ws0">实验<span class="_ _0"> </span><span class="ff2">2</span></div><div class="t m0 x7 h3 y15 ff1 fs0 fc0 sc0 ls0 ws0">由积分定义的序列</div></div><div class="c x8 y16 w3 h8"><div class="t m1 x9 h9 y17 ff2 fs4 fc0 sc0 ls0 ws0">...<span class="_ _b"></span>2<span class="_ _c"></span>,<span class="_ _d"></span>1<span class="_ _e"></span>,</div><div class="t m2 xa ha y18 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m2 xb ha y19 ff2 fs5 fc0 sc0 ls0 ws0">0</div><div class="t m2 xc ha y1a ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m1 xd hb y17 ff4 fs4 fc0 sc0 ls0 ws0"><span class="_ _f"></span></div><div class="t m3 xe hc y1b ff4 fs6 fc0 sc0 ls0 ws0"></div><div class="t m2 xf hd y1a ff4 fs5 fc0 sc0 ls0 ws0"></div><div class="t m1 x10 h9 y17 ff5 fs4 fc0 sc0 ls0 ws0">n<span class="_ _10"></span>dx<span class="_ _11"></span>e<span class="_ _12"></span>x<span class="_ _13"></span>I</div><div class="t m2 x11 ha y1a ff5 fs5 fc0 sc0 ls0 ws0">x<span class="_ _14"></span>n</div><div class="t m2 x12 ha y1c ff5 fs5 fc0 sc0 ls0 ws0">n</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x7 h3 y1d ff1 fs0 fc0 sc0 ls0 ws0">计算序列<span class="ff2">{</span></div></div><div class="c x13 y1e w4 he"><div class="t m4 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m5 x14 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">I</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x15 h3 y1d ff2 fs0 fc0 sc0 ls0 ws0">}<span class="ff1">有两种方法。</span></div><div class="t m0 x3 h3 y21 ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">I</span>）：</div></div><div class="c x16 y22 w5 he"><div class="t m0 x17 h10 y20 ff2 fs0 fc0 sc0 ls0 ws0">,...<span class="_ _15"></span>3<span class="_ _16"></span>,<span class="_ _16"></span>2<span class="_ _11"></span>,<span class="_ _17"></span>1<span class="_ _18"></span>,<span class="_ _19"></span>/<span class="_ _1a"></span>1</div><div class="t m0 x18 hf y1f ff2 fs7 fc0 sc0 ls0 ws0">1<span class="_ _1b"></span>1</div><div class="t m0 x19 h11 y20 ff4 fs0 fc0 sc0 ls0 ws0"><span class="_ _1c"></span><span class="_ _1d"></span><span class="_ _1e"></span></div><div class="t m0 x1a h12 y1f ff4 fs7 fc0 sc0 ls0 ws0"></div><div class="t m0 x4 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">n<span class="_ _1f"></span>nI<span class="_ _20"></span>I<span class="_ _14"></span>e<span class="_ _21"></span>I</div><div class="t m0 x1b hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n<span class="_ _22"></span>n</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3 h3 y23 ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">II</span>）：</div></div><div class="c x1c y24 w6 h13"><div class="t m1 x1d h9 y25 ff2 fs4 fc0 sc0 ls0 ws0">2<span class="_ _c"></span>,<span class="_ _23"></span>3<span class="_ _24"></span>,..<span class="_ _2"></span>.<span class="_ _24"></span>2<span class="_ _25"></span>,<span class="_ _d"></span>1<span class="_ _26"></span>,<span class="_ _27"></span>,</div><div class="t m1 x1e h9 y26 ff2 fs4 fc0 sc0 ls0 ws0">1</div><div class="t m1 x1f h9 y25 ff2 fs4 fc0 sc0 ls0 ws0">,<span class="_ _16"></span>0</div><div class="t m2 x20 ha y17 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m1 x21 hb y25 ff4 fs4 fc0 sc0 ls0 ws0"><span class="_ _1f"></span><span class="_ _28"></span></div><div class="t m1 x10 hb y26 ff4 fs4 fc0 sc0 ls0 ws0"></div><div class="t m1 x22 hb y25 ff4 fs4 fc0 sc0 ls0 ws0"><span class="_ _29"></span></div><div class="t m2 x11 hd y17 ff4 fs5 fc0 sc0 ls0 ws0"></div><div class="t m1 x23 h9 y25 ff5 fs4 fc0 sc0 ls0 ws0">N<span class="_ _21"></span>N<span class="_ _2a"></span>N<span class="_ _2b"></span>n</div><div class="t m1 x24 h9 y27 ff5 fs4 fc0 sc0 ls0 ws0">n</div><div class="t m1 xd h9 y26 ff5 fs4 fc0 sc0 ls0 ws0">E</div><div class="t m1 x25 h9 y25 ff5 fs4 fc0 sc0 ls0 ws0">E<span class="_ _2c"></span>E</div><div class="t m2 x1a ha y28 ff5 fs5 fc0 sc0 ls0 ws0">n</div><div class="t m2 x26 ha y17 ff5 fs5 fc0 sc0 ls0 ws0">n<span class="_ _17"></span>N</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3 h5 y29 ff1 fs2 fc0 sc1 ls0 ws0">题目</div><div class="t m0 x3 h3 y2a ff1 fs0 fc0 sc0 ls0 ws0">误差分析</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6268ca104f8811599e18655b/bg2.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0">班级：自动化<span class="_ _0"> </span><span class="ff2">1501 </span>姓名：付力<span class="ff2"> </span>学号：<span class="ff2">2015307201308</span></div><div class="t m0 x3 h5 y2b ff1 fs2 fc0 sc1 ls0 ws0">实验要求</div><div class="t m0 x3 h3 y2c ff1 fs0 fc0 sc0 ls0 ws0">实验<span class="_ _0"> </span><span class="ff2">1</span></div><div class="t m0 x7 h3 y2d ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">1</span>）<span class="_ _2d"> </span>选<span class="_ _2"></span>择<span class="_ _2"></span>充<span class="_ _2"></span>分<span class="_ _2"></span>小<span class="_ _2"></span>的<span class="_ _9"> </span><span class="ff2">es<span class="_ _1"></span>s<span class="_ _2"></span><span class="ff1">，<span class="_ _2"></span>反<span class="_ _7"></span>复进<span class="_ _2"></span>行<span class="_ _2"></span>上<span class="_ _7"></span>述实<span class="_ _7"></span>验，<span class="_ _7"></span>记录<span class="_ _7"></span>结果<span class="_ _7"></span>的变<span class="_ _2"></span>化<span class="_ _2"></span>并<span class="_ _7"></span>分</span></span></div><div class="t m0 x17 h3 y5 ff1 fs0 fc0 sc0 ls0 ws0">析<span class="_ _2"></span>它们<span class="_ _2"></span>。<span class="_ _2"></span>如<span class="_ _2"></span>果<span class="_ _2"></span>扰<span class="_ _2"></span>动项<span class="_ _2"></span>的<span class="_ _2"></span>系<span class="_ _2"></span>数<span class="_ _2e"> </span>很小<span class="_ _2"></span>，<span class="_ _2"></span>我<span class="_ _2"></span>们<span class="_ _2"></span>自<span class="_ _2"></span>然感<span class="_ _2"></span>觉<span class="_ _2"></span>（<span class="_ _2"></span><span class="ff2">1.1<span class="_ _2"></span></span>）<span class="_ _2"></span>和<span class="_ _2"></span>（<span class="_ _2"></span><span class="ff2">1.2<span class="_ _2"></span></span>）</div><div class="t m0 x17 h3 y2e ff1 fs0 fc0 sc0 ls0 ws0">的解应当相差很小。计算中你有什么出乎意料的发现？表明有些解关</div><div class="t m0 x17 h3 y2f ff1 fs0 fc0 sc0 ls0 ws0">于如此的扰动敏感性如何？</div><div class="t m0 x7 h3 y7 ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">2</span>）<span class="_ _2d"> </span>将<span class="_ _2"></span>方<span class="_ _2"></span>程<span class="_ _2"></span>（<span class="_ _7"></span><span class="ff2">1.2<span class="_ _2"></span></span>）<span class="_ _2"></span>中<span class="_ _2"></span>的<span class="_ _2"></span>扰<span class="_ _7"></span>动项<span class="_ _7"></span>改成<span class="_ _2f"> </span>或<span class="_ _2"></span>其<span class="_ _2"></span>它<span class="_ _2"></span>形<span class="_ _2"></span>式<span class="_ _7"></span>，实<span class="_ _7"></span>验中<span class="_ _7"></span>又有</div><div class="t m0 x17 h3 y30 ff1 fs0 fc0 sc0 ls0 ws0">怎样的现象出现？</div><div class="t m0 x3 h3 y31 ff1 fs0 fc0 sc0 ls0 ws0">实验<span class="_ _0"> </span><span class="ff2">2</span></div><div class="t m0 x3 h3 y32 ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">1</span>）分别用算法（<span class="_ _2"></span><span class="ff2">I</span>）、（<span class="_ _30"> </span><span class="ff2">II</span>）并在计算中分别采用<span class="_ _8"> </span><span class="ff2">5<span class="_ _5"> </span></span>位、<span class="_ _2"></span><span class="ff2">6<span class="_ _0"> </span></span>位和<span class="_ _0"> </span><span class="ff2">7<span class="_ _0"> </span></span>位有效数字，</div><div class="t m0 x3 h3 y33 ff1 fs0 fc0 sc0 ls0 ws0">请判断哪种算法能给出更精确的结果。</div><div class="t m0 x3 h3 y34 ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">2</span>）两种算法的优劣，与你的第一感觉是否吻合。请从理论上证明你实验得出</div><div class="t m0 x3 h3 y35 ff1 fs0 fc0 sc0 ls0 ws0">的结果，解<span class="_ _2"></span>释实验的结果。算<span class="_ _2"></span>法（<span class="_ _7"></span><span class="ff2">I</span>）中的</div></div><div class="c x27 y36 w7 h14"><div class="t m6 x28 ha y37 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m7 x14 h9 y38 ff5 fs4 fc0 sc0 ls0 ws0">I</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x29 h3 y35 ff1 fs0 fc0 sc0 ls0 ws0">的计算误差为</div></div><div class="c x2a y36 w7 h14"><div class="t m6 x28 ha y37 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m7 x14 h9 y38 ff5 fs4 fc0 sc0 ls0 ws0">e</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x2b h3 y35 ff1 fs0 fc0 sc0 ls0 ws0">，由</div></div><div class="c x2c y36 w8 h14"><div class="t m6 x28 ha y37 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m7 x14 h9 y38 ff5 fs4 fc0 sc0 ls0 ws0">I</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x2d h3 y35 ff1 fs0 fc0 sc0 ls0 ws0">递推计算</div></div><div class="c x2e y36 w4 he"><div class="t m4 x28 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m5 x14 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">I</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3 h3 y39 ff1 fs0 fc0 sc0 ls0 ws0">的<span class="_ _2"></span>误<span class="_ _2"></span>差<span class="_ _2"></span>为</div></div><div class="c x1c y3a w4 he"><div class="t m4 x28 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m5 x14 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">e</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y39 ff1 fs0 fc0 sc0 ls0 ws0">；<span class="_ _2"></span>算<span class="_ _2"></span>法<span class="_ _2"></span>（<span class="_ _7"></span><span class="ff2">II<span class="_ _2"></span></span>）<span class="_ _2"></span>中</div></div><div class="c x2f y3a w9 he"><div class="t m0 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">N</div><div class="t m8 x14 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">I</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x30 h3 y39 ff1 fs0 fc0 sc0 ls0 ws0">的<span class="_ _2"></span>计<span class="_ _2"></span>算<span class="_ _2"></span>误<span class="_ _2"></span>差<span class="_ _7"></span>为</div></div><div class="c x29 y3a wa he"><div class="t m9 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">N</div><div class="t ma x31 h15 y20 ff4 fs8 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x32 h3 y39 ff1 fs0 fc0 sc0 ls0 ws0">，<span class="_ _2"></span>由</div></div><div class="c x33 y3a w9 he"><div class="t m0 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">N</div><div class="t m8 x14 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">I</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x34 h3 y39 ff1 fs0 fc0 sc0 ls0 ws0">向<span class="_ _2"></span>前<span class="_ _2"></span>递<span class="_ _2"></span>推<span class="_ _2"></span>计<span class="_ _7"></span>算</div></div><div class="c x35 y3a wb he"><div class="t m8 x36 h10 y20 ff2 fs0 fc0 sc0 ls0 ws0">)<span class="_ _31"></span>(<span class="_ _32"> </span><span class="ff5">N<span class="_ _33"></span>n<span class="_ _34"></span>I</span></div><div class="t m0 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m8 xe h11 y20 ff4 fs0 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3 h3 y3b ff1 fs0 fc0 sc0 ls0 ws0">的误差为</div></div><div class="c x37 y3c wc he"><div class="t mb x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t mc x31 h16 y20 ff4 fs9 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y3b ff1 fs0 fc0 sc0 ls0 ws0">。如果在上<span class="_ _2"></span>述两算法中都假定<span class="_ _2"></span>后面的计算不<span class="_ _2"></span>再引入其他误差，<span class="_ _7"></span><span class="ff2"> <span class="_ _2"></span></span>试给</div><div class="t m0 x3 h3 y3d ff1 fs0 fc0 sc0 ls0 ws0">出</div></div><div class="c x18 y3e w4 he"><div class="t m4 x28 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m5 x31 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">e</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x38 h3 y3d ff1 fs0 fc0 sc0 ls0 ws0">与</div></div><div class="c x39 y3e w7 h14"><div class="t m6 x28 ha y37 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m7 x31 h9 y38 ff5 fs4 fc0 sc0 ls0 ws0">e</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x37 h3 y3d ff1 fs0 fc0 sc0 ls0 ws0">的关系和</div></div><div class="c x3a y3e wc he"><div class="t mb x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t mc x31 h16 y20 ff4 fs9 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3b h3 y3d ff1 fs0 fc0 sc0 ls0 ws0">与</div></div><div class="c x3c y3e wa he"><div class="t m9 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">N</div><div class="t ma x31 h15 y20 ff4 fs8 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3d h3 y3d ff1 fs0 fc0 sc0 ls0 ws0">的关系。</div><div class="t m0 x3 h3 y3f ff1 fs0 fc0 sc0 ls0 ws0">（<span class="ff2">3</span>）算法<span class="_ _2"></span>（<span class="ff2">I</span>）中通常</div></div><div class="c x3e y40 w7 h14"><div class="t m6 x28 ha y37 ff2 fs5 fc0 sc0 ls0 ws0">1</div><div class="t m7 x31 h9 y38 ff5 fs4 fc0 sc0 ls0 ws0">e</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x3f h3 y3f ff1 fs0 fc0 sc0 ls0 ws0">会很小，当<span class="_ _0"> </span><span class="ff2">n<span class="_ _8"> </span></span>增大时，</div></div><div class="c x32 y40 w4 he"><div class="t m4 x28 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t m5 x31 h10 y20 ff5 fs0 fc0 sc0 ls0 ws0">e</div></div><div class="c x0 y1 w2 h2"><div class="t m0 x40 h3 y3f ff1 fs0 fc0 sc0 ls0 ws0">的变化趋势<span class="_ _2"></span>如何？算法（<span class="_ _2"></span><span class="ff2">II</span>）</div><div class="t m0 x3 h3 y41 ff1 fs0 fc0 sc0 ls0 ws0">中</div></div><div class="c x18 y42 wd he"><div class="t m9 x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">N</div><div class="t ma x31 h15 y20 ff4 fs8 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x41 h3 y41 ff1 fs0 fc0 sc0 ls0 ws0">通常相对比较<span class="_ _2"></span>大，当<span class="_ _8"> </span><span class="ff2">n<span class="_ _0"> </span></span>减小时，<span class="_ _2"></span>误差</div></div><div class="c x42 y42 wc he"><div class="t mb x12 hf y1f ff5 fs7 fc0 sc0 ls0 ws0">n</div><div class="t mc x31 h16 y20 ff4 fs9 fc0 sc0 ls0 ws0"></div></div><div class="c x0 y1 w2 h2"><div class="t m0 x29 h3 y41 ff1 fs0 fc0 sc0 ls0 ws0">又是如何传<span class="_ _2"></span>播的？也就是说比<span class="_ _2"></span>较一</div><div class="t m0 x3 h3 y43 ff1 fs0 fc0 sc0 ls0 ws0">下上<span class="_ _2"></span>述<span class="_ _2"></span>两个<span class="_ _2"></span>算<span class="_ _2"></span>法，<span class="_ _2"></span>当<span class="_ _2"></span>某一<span class="_ _2"></span>步<span class="_ _2"></span>产生<span class="_ _2"></span>误<span class="_ _2"></span>差后<span class="_ _2"></span>，<span class="_ _2"></span>该误<span class="_ _2"></span>差<span class="_ _2"></span>对<span class="_ _2"></span>后面<span class="_ _2"></span>的<span class="_ _2"></span>影响<span class="_ _2"></span>是<span class="_ _2"></span>衰减<span class="_ _2"></span>还<span class="_ _2"></span>是扩<span class="_ _2"></span>张</div><div class="t m0 x3 h3 y44 ff1 fs0 fc0 sc0 ls0 ws0">的。</div><div class="t m0 x3 h6 y13 ff1 fs3 fc0 sc0 ls0 ws0">（<span class="ff2">4</span>）通过理论分析与计算实验，针对算法（<span class="ff2">I</span>）和（<span class="ff2">II</span>）的稳定性，给出结论。</div><div class="t m0 x3 h5 y45 ff1 fs2 fc0 sc1 ls0 ws0">程序<span class="ff2 sc0"> </span></div><div class="t m0 x3 h3 y46 ff1 fs0 fc0 sc0 ls0 ws0">实验<span class="_ _0"> </span><span class="ff2">1</span></div><div class="t m0 x18 h3 y47 ff1 fs0 fc0 sc0 ls0 ws0">程序<span class="_ _0"> </span><span class="ff2">1</span></div><div class="t m0 x3 h17 y48 ff6 fsa fc0 sc0 ls0 ws0">ess=0.000000001;</div><div class="t m0 x3 h17 y49 ff6 fsa fc0 sc0 ls0 ws0">ve=zeros(1,21);</div><div class="t m0 x3 h17 y4a ff6 fsa fc0 sc0 ls0 ws0">ve(2)=ess;</div><div class="t m0 x3 h17 y4b ff6 fsa fc0 sc0 ls0 ws0">roots(poly(1:20)+ve)</div><div class="t m0 x18 h3 y4c ff1 fs0 fc0 sc0 ls0 ws0">程序<span class="_ _0"> </span><span class="ff2">2</span></div><div class="t m0 x3 h17 y4d ff6 fsa fc0 sc0 ls0 ws0">ess=0.00000000001;</div><div class="t m0 x3 h17 y4e ff6 fsa fc0 sc0 ls0 ws0">ve=zeros(1,21);</div><div class="t m0 x3 h17 y4f ff6 fsa fc0 sc0 ls0 ws0">ve(2)=ess;</div><div class="t m0 x3 h17 y50 ff6 fsa fc0 sc0 ls0 ws0">roots(poly(1:20)+ve)</div><div class="t m0 x18 h3 y51 ff1 fs0 fc0 sc0 ls0 ws0">程序<span class="_ _0"> </span><span class="ff2">3</span></div><div class="t m0 x3 h17 y52 ff6 fsa fc0 sc0 ls0 ws0">ess=0.0000000000001;</div><div class="t m0 x3 h17 y53 ff6 fsa fc0 sc0 ls0 ws0">ve=zeros(1,21);</div></div></div><div class="pi" data-data='{"ctm":[1.611850,0.000000,0.000000,1.611850,0.000000,0.000000]}'></div></div>
