範例：Thiele 內插與遞歸

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範例：Thiele 內插與遞歸

由於萃取了 Thiele 係數，因此使用 Thielecoeff 與 Thiele 函數可視為遞歸技術。

1. 輸入一組量測數據，表示水沸騰的飽和溫度 (以 °C 為單位)。

2. 使用 Thiele 方法穿過數據集內插曲線。

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        <id label="Function" xml:space="preserve" label-is-contextual="true">Thiele</id>
        <sequence>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">P</id>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">coeff</id>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">x</id>
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3. 使用多項式遞歸方法透過數據集擬合曲線。

4. 繪製數據集與兩條內插曲線。

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      </traces>
      <graph-size width="457.399999999999" height="230.4" />
      <axes>
        <xAxis rank="1" legend-position="PlotBoundaryBottom" start="0" end="220">
          <axisLine position="bottom" positionticmark="-1" legendWidth="92.1466666666667" />
          <axisGrid>
            <gridFrequency>12</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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          <axisLabel />
          <markers />
          <plotEquations>
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                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">P</id>
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            </plotEquation>
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                <id xml:space="preserve" xmlns="http://schemas.mathsoft.com/math50">range</id>
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          </xyDomain>
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        <yAxis rank="1" legend-position="PlotBoundaryLeft" start="290" end="675">
          <axisLine position="origin" positionticmark="0" legendWidth="97.29" />
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            <gridFrequency>12</gridFrequency>
            <gridLabels display="true" />
            <gridLines />
            <tickMarks display="true" />
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5. 比較 Thiele 方法傳回的計算結果與蒸汽表的兩個中點。

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    <eval xmlns="http://schemas.mathsoft.com/math50">
      <matrix rows="3" cols="2">
        <str xml:space="preserve"> mid-points </str>
        <apply>
          <scale />
          <real>290.52</real>
          <id label="Unit" xml:space="preserve" label-is-contextual="true">°C</id>
        </apply>
        <apply>
          <scale />
          <real>327.78</real>
          <id label="Unit" xml:space="preserve" label-is-contextual="true">°C</id>
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          <id label="Variable" xml:space="preserve" label-is-contextual="true">TI</id>
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            <real>75</real>
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        <apply>
          <id label="Variable" xml:space="preserve" label-is-contextual="true">TI</id>
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            <real>125</real>
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      <decimal precision="3" show-trailing-zeros="false" radix="dec" imaginary-value="i" />
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計算的數據點會與已發行的數據十分相符。

6. 使用 Thiele 內插曲線，計算在水平面以上 2250 公尺的墨西哥市內水沸騰的溫度。

參照

International Association for the Properties of Water and Steam，網址為 http://www.iapws.org

相關主題

Thiele 連續分數內插

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