uTools-Manuals/docs/python/cmath.html

<div class="body" role="main"><div class="section" id="module-cmath"><h1><span class="yiyi-st" id="yiyi-10">9.3. <a class="reference internal" href="#module-cmath" title="cmath: Mathematical functions for complex numbers."><code class="xref py py-mod docutils literal"><span class="pre">cmath</span></code></a>  - 复数的数学函数</span></h1><p><span class="yiyi-st" id="yiyi-11">本模块始终是可用的。</span><span class="yiyi-st" id="yiyi-12">它提供对数学函数为复数的访问。</span><span class="yiyi-st" id="yiyi-13">本模块中的函数作为参数接受整数、 浮点数或复数。</span><span class="yiyi-st" id="yiyi-14">它们还将接受具有<a class="reference internal" href="../reference/datamodel.html#object.__complex__" title="object.__complex__"><code class="xref py py-meth docutils literal"><span class="pre">__complex__()</span></code></a>或<a class="reference internal" href="../reference/datamodel.html#object.__float__" title="object.__float__"><code class="xref py py-meth docutils literal"><span class="pre">__float__()</span></code></a>方法的任何Python对象：这些方法用于将对象转换为复杂或浮点数字，然后将该函数应用于转换的结果。</span></p><div class="admonition note"><p class="first admonition-title"><span class="yiyi-st" id="yiyi-15">注</span></p><p class="last"><span class="yiyi-st" id="yiyi-16">在平台上的硬件和系统级支持签名的零，涉及分支函数是连续的<em>两边的分支切割</em>： 零的标志区分的分支切割从另一侧。</span><span class="yiyi-st" id="yiyi-17">在做的平台上不支持签署的零的连续性是作为以下指定的内容。</span></p></div><div class="section" id="conversions-to-and-from-polar-coordinates"><h2><span class="yiyi-st" id="yiyi-18">9.3.1.</span><span class="yiyi-st" id="yiyi-19">极坐标的转换</span></h2><p><span class="yiyi-st" id="yiyi-20">使用<em>矩形</em>或<em>笛卡尔</em>坐标在内部存储Python复杂数<code class="docutils literal"><span class="pre">z</span></code>。</span><span class="yiyi-st" id="yiyi-21">它完全由其<em>实部</em> <code class="docutils literal"><span class="pre">z.real</span></code>及其<em>虚部</em> <code class="docutils literal"><span class="pre">z.imag</span></code>决定。</span><span class="yiyi-st" id="yiyi-22">换句话说：</span></p><pre><code class="language-python"><span></span><span class="n">z</span> <span class="o">==</span> <span class="n">z</span><span class="o">.</span><span class="n">real</span> <span class="o">+</span> <span class="n">z</span><span class="o">.</span><span class="n">imag</span><span class="o">*</span><span class="mi">1</span><span class="n">j</span>
</code></pre><p><span class="yiyi-st" id="yiyi-23"><em>极坐标</em>给另一种方法来表示一个复杂的数字。</span><span class="yiyi-st" id="yiyi-24">在极坐标下，复数<em>z</em>是由弹性模量<em>r</em>和相角<em>φ</em>定义的。</span><span class="yiyi-st" id="yiyi-25">弹性模量<em>r</em>是从<em>z</em>到原点的距离而阶段<em>皮皮</em>是逆时针旋转的角度，以弧度为单位），从积极的 x 轴到联接到<em>z</em>的原点的直线段测量。</span></p><p><span class="yiyi-st" id="yiyi-26">以下功能可以用于从本机的矩形坐标转换到极坐标或进行相反的转换。</span></p><dl class="function"><dt id="cmath.phase"><span class="yiyi-st" id="yiyi-27"><code class="descclassname">cmath.</code><code class="descname">phase</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-28">返回阶段的<em>x</em> （也被称为<em>参数</em>的<em>x</em>），作为一个浮点数。</span><span class="yiyi-st" id="yiyi-29"><code class="docutils literal"><span class="pre">phase(x)</span></code>等效于<code class="docutils literal"><span class="pre">math.atan2（x.imag，</span> <span class="pre">x.real）</span></code>。</span><span class="yiyi-st" id="yiyi-30">结果谎言在范围 [-π π]，并削减此操作谎言沿负实轴连续从上面的分支。</span><span class="yiyi-st" id="yiyi-31">在支持有符号零（包括当前使用的大多数系统）的系统上，这意味着结果的符号与<code class="docutils literal"><span class="pre">x.imag</span></code>的符号相同，即使是<code class="docutils literal"><span class="pre">x.imag</span></code>为零：</span></p><pre><code class="language-python"><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">phase</span><span class="p">(</span><span class="nb">complex</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">))</span>
<span class="go">3.141592653589793</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">phase</span><span class="p">(</span><span class="nb">complex</span><span class="p">(</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0</span><span class="p">))</span>
<span class="go">-3.141592653589793</span>
</code></pre></dd></dl><div class="admonition note"><p class="first admonition-title"><span class="yiyi-st" id="yiyi-32">注</span></p><p class="last"><span class="yiyi-st" id="yiyi-33">复数<em>x</em>的模数（绝对值）可以使用内建<a class="reference internal" href="functions.html#abs" title="abs"><code class="xref py py-func docutils literal"><span class="pre">abs()</span></code></a>函数计算。</span><span class="yiyi-st" id="yiyi-34">此操作没有单独的<a class="reference internal" href="#module-cmath" title="cmath: Mathematical functions for complex numbers."><code class="xref py py-mod docutils literal"><span class="pre">cmath</span></code></a>模块函数。</span></p></div><dl class="function"><dt id="cmath.polar"><span class="yiyi-st" id="yiyi-35"><code class="descclassname">cmath.</code><code class="descname">polar</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-36">返回在极坐标系中的<em>x</em>表示。</span><span class="yiyi-st" id="yiyi-37">Returns a pair <code class="docutils literal"><span class="pre">(r,</span> <span class="pre">phi)</span></code> where <em>r</em> is the modulus of <em>x</em> and phi is the phase of <em>x</em>. <code class="docutils literal"><span class="pre">polar(x)</span></code> is equivalent to <code class="docutils literal"><span class="pre">(abs(x),</span> <span class="pre">phase(x))</span></code>.</span></p></dd></dl><dl class="function"><dt id="cmath.rect"><span class="yiyi-st" id="yiyi-38"><code class="descclassname">cmath.</code><code class="descname">rect</code><span class="sig-paren">(</span><em>r</em>, <em>phi</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-39">返回复数<em>x</em>用极坐标<em>r</em>和<em>phi</em>。</span><span class="yiyi-st" id="yiyi-40">等于<code class="docutils literal"><span class="pre">r</span> <span class="pre">*</span> <span class="pre">（math.cos（phi）</span> <span class="pre">+</span> <span class="pre">math.sin phi）* 1j）</span></code>。</span></p></dd></dl></div><div class="section" id="power-and-logarithmic-functions"><h2><span class="yiyi-st" id="yiyi-41">9.3.2.</span><span class="yiyi-st" id="yiyi-42">幂函数和对数函数</span></h2><dl class="function"><dt id="cmath.exp"><span class="yiyi-st" id="yiyi-43"><code class="descclassname">cmath.</code><code class="descname">exp</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-44">返回指数值<code class="docutils literal"><span class="pre">e**x</span></code>。</span></p></dd></dl><dl class="function"><dt id="cmath.log"><span class="yiyi-st" id="yiyi-45"><code class="descclassname">cmath.</code><code class="descname">log</code><span class="sig-paren">(</span><em>x</em><span class="optional">[</span>, <em>base</em><span class="optional">]</span><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-46">返回给定<em>基</em>的<em>x</em>的对数。</span><span class="yiyi-st" id="yiyi-47">如果未指定的<em>基地</em>，返回<em>x</em>的自然对数。</span><span class="yiyi-st" id="yiyi-48">那里是一个分支切断，从 0 到-∞，负实轴沿连续从上面。</span></p></dd></dl><dl class="function"><dt id="cmath.log10"><span class="yiyi-st" id="yiyi-49"><code class="descclassname">cmath.</code><code class="descname">log10</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-50">返回<em>x</em>的对数。</span><span class="yiyi-st" id="yiyi-51">这具有与<a class="reference internal" href="#cmath.log" title="cmath.log"><code class="xref py py-func docutils literal"><span class="pre">log()</span></code></a>相同的分支切割。</span></p></dd></dl><dl class="function"><dt id="cmath.sqrt"><span class="yiyi-st" id="yiyi-52"><code class="descclassname">cmath.</code><code class="descname">sqrt</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-53">返回<em>x</em>的平方根。</span><span class="yiyi-st" id="yiyi-54">这具有与<a class="reference internal" href="#cmath.log" title="cmath.log"><code class="xref py py-func docutils literal"><span class="pre">log()</span></code></a>相同的分支切割。</span></p></dd></dl></div><div class="section" id="trigonometric-functions"><h2><span class="yiyi-st" id="yiyi-55">9.3.3.</span><span class="yiyi-st" id="yiyi-56">三角函数</span></h2><dl class="function"><dt id="cmath.acos"><span class="yiyi-st" id="yiyi-57"><code class="descclassname">cmath.</code><code class="descname">acos</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-58">返回<em>x</em>的反余弦。</span><span class="yiyi-st" id="yiyi-59">有两个分支割痕： 一个延伸权从 1 沿着实轴到 ∞，连续从下面。</span><span class="yiyi-st" id="yiyi-60">其他左延伸从沿着实轴-1 至-∞，连续从上面。</span></p></dd></dl><dl class="function"><dt id="cmath.asin"><span class="yiyi-st" id="yiyi-61"><code class="descclassname">cmath.</code><code class="descname">asin</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-62">返回<em>x</em>的反正弦值。</span><span class="yiyi-st" id="yiyi-63">这具有与<a class="reference internal" href="#cmath.acos" title="cmath.acos"><code class="xref py py-func docutils literal"><span class="pre">acos()</span></code></a>相同的分支切口。</span></p></dd></dl><dl class="function"><dt id="cmath.atan"><span class="yiyi-st" id="yiyi-64"><code class="descclassname">cmath.</code><code class="descname">atan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-65">返回<em>x</em>的反正切值。</span><span class="yiyi-st" id="yiyi-66">有两个分支切口：一个从<code class="docutils literal"><span class="pre">1j</span></code>沿虚轴延伸到<code class="docutils literal"><span class="pre">∞j</span></code>，从右边连续。</span><span class="yiyi-st" id="yiyi-67">另一个从<code class="docutils literal"><span class="pre">-1j</span></code>沿虚轴延伸到从左边连续的<code class="docutils literal"><span class="pre">-∞j</span></code>。</span></p></dd></dl><dl class="function"><dt id="cmath.cos"><span class="yiyi-st" id="yiyi-68"> <code class="descclassname">cmath.</code><code class="descname">cos</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-69">返回<em>x</em>的余弦值。</span></p></dd></dl><dl class="function"><dt id="cmath.sin"><span class="yiyi-st" id="yiyi-70"><code class="descclassname">cmath.</code><code class="descname">sin</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-71">返回<em>x</em>的正弦值。</span></p></dd></dl><dl class="function"><dt id="cmath.tan"><span class="yiyi-st" id="yiyi-72"><code class="descclassname">cmath.</code><code class="descname">tan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-73">返回<em>x</em>的正切值。</span></p></dd></dl></div><div class="section" id="hyperbolic-functions"><h2><span class="yiyi-st" id="yiyi-74">9.3.4.</span><span class="yiyi-st" id="yiyi-75">双曲函数</span></h2><dl class="function"><dt id="cmath.acosh"><span class="yiyi-st" id="yiyi-76"><code class="descclassname">cmath.</code><code class="descname">acosh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-77">返回<em>x</em>的反双曲余弦值。</span><span class="yiyi-st" id="yiyi-78">那里是一个分支切割，从 1 沿着实轴左延伸到-∞，连续从上面。</span></p></dd></dl><dl class="function"><dt id="cmath.asinh"><span class="yiyi-st" id="yiyi-79"><code class="descclassname">cmath.</code><code class="descname">asinh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-80">返回<em>x</em>的反双曲正弦值。</span><span class="yiyi-st" id="yiyi-81">有两个分支切口：一个从<code class="docutils literal"><span class="pre">1j</span></code>沿虚轴延伸到<code class="docutils literal"><span class="pre">∞j</span></code>，从右边连续。</span><span class="yiyi-st" id="yiyi-82">另一个从<code class="docutils literal"><span class="pre">-1j</span></code>沿虚轴延伸到从左边连续的<code class="docutils literal"><span class="pre">-∞j</span></code>。</span></p></dd></dl><dl class="function"><dt id="cmath.atanh"><span class="yiyi-st" id="yiyi-83"><code class="descclassname">cmath.</code><code class="descname">atanh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-84">返回<em>x</em>的反双曲正切值。</span><span class="yiyi-st" id="yiyi-85">有两个分支切口：一个从<code class="docutils literal"><span class="pre">1</span></code>沿着实轴延伸到<code class="docutils literal"><span class="pre">∞</span></code>，从下面连续。</span><span class="yiyi-st" id="yiyi-86">另一个从<code class="docutils literal"><span class="pre">-1</span></code>沿着实轴延伸到<code class="docutils literal"><span class="pre">-∞</span></code>，从上方连续。</span></p></dd></dl><dl class="function"><dt id="cmath.cosh"><span class="yiyi-st" id="yiyi-87"><code class="descclassname">cmath.</code><code class="descname">cosh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-88">返回<em>x</em>的双曲余弦值。</span></p></dd></dl><dl class="function"><dt id="cmath.sinh"><span class="yiyi-st" id="yiyi-89"><code class="descclassname">cmath.</code><code class="descname">sinh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-90">返回<em>x</em>的双曲正弦值。</span></p></dd></dl><dl class="function"><dt id="cmath.tanh"><span class="yiyi-st" id="yiyi-91"> <code class="descclassname">cmath.</code><code class="descname">tanh</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-92">返回<em>x</em>的双曲正切值。</span></p></dd></dl></div><div class="section" id="classification-functions"><h2><span class="yiyi-st" id="yiyi-93">9.3.5.</span><span class="yiyi-st" id="yiyi-94">分类函数</span></h2><dl class="function"><dt id="cmath.isfinite"><span class="yiyi-st" id="yiyi-95"> <code class="descclassname">cmath.</code><code class="descname">isfinite</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-96">如果<em>x</em>的实部和虚部都是有限的，则返回<code class="docutils literal"><span class="pre">True</span></code>，否则返回<code class="docutils literal"><span class="pre">False</span></code>。</span></p><div class="versionadded"><p><span class="yiyi-st" id="yiyi-97"><span class="versionmodified">版本3.2中的新功能。</span></span></p></div></dd></dl><dl class="function"><dt id="cmath.isinf"><span class="yiyi-st" id="yiyi-98"><code class="descclassname">cmath.</code><code class="descname">isinf</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-99">如果<em>x</em>的实部或虚部是无穷大，而<code class="docutils literal"><span class="pre">False</span></code>则返回<code class="docutils literal"><span class="pre">True</span></code>。</span></p></dd></dl><dl class="function"><dt id="cmath.isnan"><span class="yiyi-st" id="yiyi-100"><code class="descclassname">cmath.</code><code class="descname">isnan</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-101">如果<em>x</em>的实部或虚部是NaN，而<code class="docutils literal"><span class="pre">False</span></code>则返回<code class="docutils literal"><span class="pre">True</span></code>。</span></p></dd></dl><dl class="function"><dt id="cmath.isclose"><span class="yiyi-st" id="yiyi-102"><code class="descclassname">cmath.</code><code class="descname">isclose</code><span class="sig-paren">(</span><em>a</em>, <em>b</em>, <em>*</em>, <em>rel_tol=1e-09</em>, <em>abs_tol=0.0</em><span class="sig-paren">)</span></span></dt><dd><p><span class="yiyi-st" id="yiyi-103">如果<em>a</em>和<em>b</em>的值彼此接近，而<code class="docutils literal"><span class="pre">False</span></code>则返回<code class="docutils literal"><span class="pre">True</span></code></span></p><p><span class="yiyi-st" id="yiyi-104">根据给定的绝对和相对容限确定两个值是否接近。</span></p><p><span class="yiyi-st" id="yiyi-105"><em>rel_tol</em>是相对容限 - 它是<em>a</em>和<em>b</em>之间的最大允许差值，相对于<em>/ t3&gt;或<em>b</em>。</em></span><span class="yiyi-st" id="yiyi-106">例如，要将公差设置为5％，请传递<code class="docutils literal"><span class="pre">rel_tol=0.05</span></code>。</span><span class="yiyi-st" id="yiyi-107">默认容差为<code class="docutils literal"><span class="pre">1e-09</span></code>，它确保两个值在大约9个十进制数字内相同。</span><span class="yiyi-st" id="yiyi-108"><em>rel_tol</em>必须大于零。</span></p><p><span class="yiyi-st" id="yiyi-109"><em>abs_tol</em>是最小绝对公差 - 对于接近零的比较有用。</span><span class="yiyi-st" id="yiyi-110"><em>abs_tol</em>必须至少为零。</span></p><p><span class="yiyi-st" id="yiyi-111">如果没有错误发生，则结果将是：<code class="docutils literal"><span class="pre">abs（ab）</span> <span class="pre"> <span class="pre">max（rel_tol</span> <span class="pre">t4&gt; <span class="pre">max（abs（a），</span> <span class="pre">abs（b）），</span> <span class="pre">abs_tol）</span></span></span></code>。</span></p><p><span class="yiyi-st" id="yiyi-112">将根据IEEE规则处理特殊值<code class="docutils literal"><span class="pre">NaN</span></code>，<code class="docutils literal"><span class="pre">inf</span></code>和<code class="docutils literal"><span class="pre">-inf</span></code>。</span><span class="yiyi-st" id="yiyi-113">具体地，不认为<code class="docutils literal"><span class="pre">NaN</span></code>接近任何其他值，包括<code class="docutils literal"><span class="pre">NaN</span></code>。</span><span class="yiyi-st" id="yiyi-114"><code class="docutils literal"><span class="pre">inf</span></code>和<code class="docutils literal"><span class="pre">-inf</span></code>只被认为接近自己。</span></p><div class="versionadded"><p><span class="yiyi-st" id="yiyi-115"><span class="versionmodified">版本3.5中的新功能。</span></span></p></div><div class="admonition seealso"><p class="first admonition-title"><span class="yiyi-st" id="yiyi-116">请参见</span></p><p class="last"><span class="yiyi-st" id="yiyi-117"><span class="target" id="index-0"></span> <a class="pep reference external" href="https://www.python.org/dev/peps/pep-0485"><strong>PEP 485</strong></a>  - 测试近似相等的函数</span></p></div></dd></dl></div><div class="section" id="constants"><h2><span class="yiyi-st" id="yiyi-118">9.3.6.</span><span class="yiyi-st" id="yiyi-119">常量</span></h2><dl class="data"><dt id="cmath.pi"><span class="yiyi-st" id="yiyi-120"><code class="descclassname">cmath.</code><code class="descname">pi</code></span></dt><dd><p><span class="yiyi-st" id="yiyi-121">数学常量<em>π</em>，作为一个浮点数。</span></p></dd></dl><dl class="data"><dt id="cmath.e"><span class="yiyi-st" id="yiyi-122"> <code class="descclassname">cmath.</code><code class="descname">e</code></span></dt><dd><p><span class="yiyi-st" id="yiyi-123">数学常数<em>e</em>，作为一个浮点数。</span></p></dd></dl><p id="index-1"><span class="yiyi-st" id="yiyi-124">请注意，函数的选择与模块<a class="reference internal" href="math.html#module-math" title="math: Mathematical functions (sin() etc.)."><code class="xref py py-mod docutils literal"><span class="pre">math</span></code></a>中的函数类似，但不完全相同。</span><span class="yiyi-st" id="yiyi-125">有两个模块的原因是一些用户不感兴趣复数，并且也许甚至不知道它们是什么。</span><span class="yiyi-st" id="yiyi-126">他们宁愿使用<code class="docutils literal"><span class="pre">math.sqrt(-1)</span></code>引发异常而不是返回一个复数。</span><span class="yiyi-st" id="yiyi-127">还要注意，<a class="reference internal" href="#module-cmath" title="cmath: Mathematical functions for complex numbers."><code class="xref py py-mod docutils literal"><span class="pre">cmath</span></code></a>中定义的函数总是返回一个复数，即使答案可以表示为一个实数（在这种情况下，复数的虚部为零）。</span></p><p><span class="yiyi-st" id="yiyi-128">分支的一个注记： 他们是沿其给定的函数不能连续的曲线。</span><span class="yiyi-st" id="yiyi-129">他们是的很多复杂的功能的必要特征。</span><span class="yiyi-st" id="yiyi-130">假设如果你需要计算复杂的功能，您将了解分支割痕。</span><span class="yiyi-st" id="yiyi-131">启蒙咨询几乎任何 （不太浅） 书上复杂的变量。</span><span class="yiyi-st" id="yiyi-132">数值用于分支削减的适当选择的信息，很好的参考应该如下：</span></p><div class="admonition seealso"><p class="first admonition-title"><span class="yiyi-st" id="yiyi-133">请参见</span></p><p class="last"><span class="yiyi-st" id="yiyi-134">Kahan，W：分支切割复杂的基本函数；或者，没有什么是符号位。</span><span class="yiyi-st" id="yiyi-135">在Iserles，A.，and Powell，M。</span><span class="yiyi-st" id="yiyi-136">（eds。</span><span class="yiyi-st" id="yiyi-137">），数值分析中的最新技术。</span><span class="yiyi-st" id="yiyi-138">克拉伦登出版社 （1987） pp165-211。</span></p></div></div></div></div>