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align-y="6" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><png item-idref="2" display-width="235.5" display-height="33" /><link href="./dataTOC.xmcd" title="Links to Table of Contents" popup="false" /><rendering item-idref="3" /></region><region region-id="513" left="90" top="44.25" width="153" height="12" align-x="90" align-y="54" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Titre" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Arial" charset="0"><u><inlineAttr line-through="false"><c val="#808000"><link href="./nonparam.xmcd" title="Links to Section Contents" popup="false"><sp count="6" />NONPARAMETRIC FITTING</link></c></inlineAttr></u></f></p></text></region><region region-id="114" left="36" top="72.75" width="123" height="13.5" align-x="36" align-y="84" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Sous-titre" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Polynomial Interpolation</p></text><indexes><phrase>polynomial interpolation</phrase><phrase>nonparametric fitting, polynomial interpolation</phrase><phrase>interpolation, polynomial</phrase></indexes></region><region region-id="583" left="66" top="97.5" width="71.25" height="12.75" align-x="66" align-y="108" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">polyint(vx,vy,x)</p></text><indexes><phrase>polyint</phrase><phrase>functions, polyint</phrase></indexes></region><region region-id="525" left="180" top="97.5" width="72.75" height="12.75" align-x="180" align-y="108" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">polycoeff(vx,vy)</p></text><indexes><phrase>polycoeff</phrase><phrase>functions, polycoeff</phrase></indexes></region><region region-id="718" left="66" top="115.5" width="93" height="12.75" align-x="78" align-y="126" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">polyiter(vx,vy,<f family="Times New Roman" charset="0">x,N,</f><f family="Symbol" charset="2" size="11"><b><inlineAttr font-style="normal" underline="false" line-through="false"><c val="#800000">e</c></inlineAttr></b></f>)</p></text><indexes><phrase>polyiter</phrase><phrase>functions, polyiter</phrase></indexes></region><region region-id="599" left="36" top="140.25" width="308.25" height="146.25" align-x="36" align-y="150" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The<f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000"> polyint</c></inlineAttr></b></f> function performs polynomial interpolation of a data set of length N at a requested point, x, using Neville's algorithm. This finds a unique polynomial of degree <region region-id="715" left="291" top="165" width="427.5" height="12.75" align-x="303.75" align-y="174" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:apply><ml:minus /><ml:id>N</ml:id><ml:real>1</ml:real></ml:apply></math><rendering item-idref="4" /></region> which passes through each point. The output is a vector of length 2 containing the interpolated value of the function and an estimate of the error. The <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polycoeff</c></inlineAttr></b></f> function will calculate the coefficients of this interpolating polynomial for use in subsequent calculations. The <inlineAttr line-through="false"><c val="#000"><f family="Verdana" charset="0"><b>polyiter</b></f></c></inlineAttr> function allows you to enter an acceptable error, <f family="Symbol" charset="2" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">e</c></inlineAttr></f>, and maximum <f family="Verdana" charset="0">degree</f> for the polynomial, allowing you to specify an interpolating polynomial of lower order, and therefore shorter calculation time, if you can accept more error.</p></text></region><region region-id="719" left="36" top="301.5" width="113.25" height="12.75" align-x="36" align-y="312" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Polynomial 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disable-calc="false"><ml:eval><ml:apply><ml:id>polyint</ml:id><ml:id>x</ml:id><ml:id>y</ml:id><ml:real>328</ml:real></ml:apply></ml:eval></math><rendering item-idref="8" /></region><region region-id="727" left="66" top="459" width="91.5" height="12.75" align-x="75" align-y="468" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:id>r</ml:id><ml:range><ml:real>0</ml:real><ml:apply><ml:minus /><ml:apply><ml:id>max</ml:id><ml:id>x</ml:id></ml:apply><ml:apply><ml:id>min</ml:id><ml:id>x</ml:id></ml:apply></ml:apply></ml:range></ml:define></math><rendering item-idref="9" /></region><region region-id="728" left="66" top="477.75" width="140.25" height="18" align-x="104.25" align-y="492" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:apply><ml:matcol /><ml:id>curve</ml:id><ml:id>r</ml:id></ml:apply><ml:apply><ml:id>polyint</ml:id><ml:id>x</ml:id><ml:id>y</ml:id><ml:apply><ml:plus /><ml:id>r</ml:id><ml:apply><ml:id>min</ml:id><ml:id>x</ml:id></ml:apply></ml:apply></ml:apply></ml:define></math><rendering item-idref="10" /></region><region region-id="726" left="0" top="510" width="6000" height="6" align-x="0" align-y="510" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="630" left="30" top="522" width="341.25" height="191.25" align-x="30" align-y="522" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><plot disable-calc="false" item-idref="11" /><rendering item-idref="12" /></region><region region-id="668" left="36" top="721.5" width="116.25" height="12.75" align-x="36" align-y="732" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Interpolation coefficients</p></text><indexes><phrase>interpolation coefficients</phrase><phrase>coefficients, interpolation</phrase></indexes></region><region region-id="797" left="36" top="746.25" width="304.5" height="72" align-x="36" align-y="756" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">If the interpolated values are all you need, it is better to stick to <b>polyint</b>. The coefficients provided by <b>polycoeff</b> are less accurate at the given data values, so they are not a good representation of interpolated values. However, if you need to calculate both the interpolating polynomial and some of its derivatives, this is a way to do it. </p></text></region><region region-id="802" left="66" top="873" width="82.5" height="18" align-x="78.75" align-y="882" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedBIUnit"><ml:apply><ml:indexer /><ml:id>c</ml:id><ml:id>i</ml:id></ml:apply><ml:apply><ml:indexer /><ml:apply><ml:id>polycoeff</ml:id><ml:id>x</ml:id><ml:id>y</ml:id></ml:apply><ml:id>i</ml:id></ml:apply></ml:define></math><rendering item-idref="13" /></region><region region-id="801" left="168" top="831" width="94.5" height="96.75" align-x="177.75" align-y="882" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:id>c</ml:id></ml:eval></math><rendering item-idref="14" /></region><region region-id="687" left="66" top="909" width="70.5" height="36" align-x="86.25" align-y="924" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>f</ml:id><ml:boundVars><ml:id>z</ml:id></ml:boundVars></ml:function><ml:apply><ml:summation /><ml:lambda><ml:boundVars><ml:id>i</ml:id></ml:boundVars><ml:parens><ml:apply><ml:mult style="default" /><ml:apply><ml:indexer /><ml:id>c</ml:id><ml:id>i</ml:id></ml:apply><ml:apply><ml:pow /><ml:id>z</ml:id><ml:id>i</ml:id></ml:apply></ml:apply></ml:parens></ml:lambda></ml:apply></ml:define></math><rendering item-idref="15" /></region><region region-id="712" left="66" top="949.5" width="57" height="29.25" align-x="90.75" align-y="966" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:function><ml:id>f1</ml:id><ml:boundVars><ml:id>z</ml:id></ml:boundVars></ml:function><ml:apply><ml:derivative /><ml:lambda><ml:boundVars><ml:id>z</ml:id></ml:boundVars><ml:apply><ml:id>f</ml:id><ml:id>z</ml:id></ml:apply></ml:lambda></ml:apply></ml:define></math><rendering item-idref="16" /></region><region region-id="729" left="0" top="990" width="6000" height="6" align-x="0" align-y="990" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="711" left="24" top="1002" width="324" height="191.25" align-x="24" align-y="1002" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><plot disable-calc="false" item-idref="17" /><rendering item-idref="18" /></region><region region-id="714" left="36" top="1196.25" width="297" height="60" align-x="36" align-y="1206" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Note that this function does not construct the polynomial of best least-squares fit, as is done by the <f family="Verdana" charset="0"><b><u><inlineAttr line-through="false"><c val="#000"><link href="./regress.xmcd" title="Links to section" popup="false">regress</link></c></inlineAttr></u></b></f> function. The results of <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyint</c></inlineAttr></b></f> and <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polycoeff </c></inlineAttr></b></f>should not be used to make predictions for y values outside of the range of original x values.</p></text></region><region region-id="798" left="36" top="1279.5" width="174.75" height="12.75" align-x="36" align-y="1290" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Aitken-Neville Iterated Interpolation </p></text><indexes><phrase>Aitken-Neville iterated interpolation</phrase><phrase>interpolation, Aitken-Neville iterated</phrase></indexes></region><region region-id="731" left="36" top="1298.25" width="295.5" height="216" align-x="36" align-y="1308" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Aitken-Neville interpolation is similar to the polynomial interpolation implemented in <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyint</c></inlineAttr></b></f> and <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polycoeff</c></inlineAttr></b></f>. But since the interpolation is iterated, <f family="Verdana" charset="0"><inlineAttr line-through="false"><b><c val="#000">polyiter</c></b></inlineAttr></f> permits the user to specify an input tolerance, <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><f family="Symbol" charset="2" size="10">e</f></inlineAttr>, and a maximum number of iterations, N, which say, in effect, that "if the last two iterated estimates of the data point agree to within the tolerance <f family="Symbol" charset="2" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">e</inlineAttr></f>, or if the number of iterations reaches the input argument N, then stop. The estimate is good enough."</p><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit" /><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Iterated interpolation is used to advantage, for example, in the Romberg quadrature of definite integrals. Numerical integration is a very computationally-intensive process. Being able to exit early can save processing time in trade for a less accurate answer.</p><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit" /><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Aitken-Neville interpolation is typically used to find only a few interpolated points with some specified tolerance.</p></text></region><region region-id="787" left="0" top="1524" width="6000" height="6" align-x="0" align-y="1524" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="751" left="36" top="1538.25" width="314.25" height="96" align-x="36" align-y="1548" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="0" text-align="inherit" list-style-type="none" tabs="inherit">The specified tolerance <f family="Symbol" charset="2">e</f> can be small enough that it forces the number of iterations to the limit N = n - 1, where n is the number of data points, or it can be large enough that the iteration is permitted to stop before the number of iterations reaches N, for some input N less than n - 1. If the number of iterations goes all the way up to n - 1, then <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyiter</c></inlineAttr></b></f> will give exactly the same results as <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyint</c></inlineAttr></b></f>. Note that the input argument N cannot be larger than n - 1.</p></text></region><region region-id="776" left="66" top="1647" width="73.5" height="12.75" align-x="79.5" align-y="1656" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedBIUnit"><ml:id>N</ml:id><ml:apply><ml:minus /><ml:apply><ml:id>length</ml:id><ml:id>x</ml:id></ml:apply><ml:real>1</ml:real></ml:apply></ml:define></math><rendering item-idref="19" /></region><region region-id="784" left="228" top="1646.25" width="29.25" height="13.5" align-x="238.5" align-y="1656" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedBIFunction"><ml:id>ε</ml:id><ml:real>.01</ml:real></ml:define></math><rendering item-idref="20" /></region><region region-id="795" left="36" top="1676.25" width="327" height="81" align-x="36" align-y="1686" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The first element of the <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyiter</c></inlineAttr></b></f> output vector is a "Converged" flag (1 = converged, 0 = did not converge). The second is the number of iterations, m<f family="Verdana" charset="0" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000"><sub>max</sub></c></inlineAttr></f>, needed to meet the specified tolerance (<b>polyint</b> always iterates up to m<sub><f family="Arial" charset="0">max</f></sub> = n - 1). The third is the iterated estimate of y obtained for the input value of x, which as noted above, will agree with <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyint</c></inlineAttr></b></f> if m<f family="Arial" charset="0"><sub>max</sub></f> = n - 1.</p></text></region><region region-id="778" left="66" top="1762.5" width="148.5" height="45.75" align-x="162" align-y="1788" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:apply><ml:id>polyiter</ml:id><ml:id>x</ml:id><ml:id>y</ml:id><ml:real>328</ml:real><ml:id>N</ml:id><ml:id>ε</ml:id></ml:apply></ml:eval></math><rendering item-idref="21" /></region><region region-id="799" left="228" top="1770.75" width="125.25" height="29.25" align-x="300.75" align-y="1788" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:eval><ml:apply><ml:id>polyint</ml:id><ml:id>x</ml:id><ml:id>y</ml:id><ml:real>328</ml:real></ml:apply></ml:eval></math><rendering item-idref="22" /></region><region region-id="791" left="36" top="1814.25" width="300.75" height="72" align-x="36" align-y="1824" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The output of polyiter tells us that to achieve an error of .01 or smaller is impossible for this algorithm at this point, because it did not converge (first return value is 0). All iterations are used, and the result is the same as that from <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyint</c></inlineAttr></b></f>. Try changing <f family="Symbol" charset="2" size="10"><inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"><c val="#000">e</c></inlineAttr></f> to .1 or 1 to see how the returns change.</p></text></region><region region-id="779" left="66" top="1893" width="91.5" height="12.75" align-x="75" align-y="1902" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:id>r</ml:id><ml:range><ml:real>0</ml:real><ml:apply><ml:minus /><ml:apply><ml:id>max</ml:id><ml:id>x</ml:id></ml:apply><ml:apply><ml:id>min</ml:id><ml:id>x</ml:id></ml:apply></ml:apply></ml:range></ml:define></math><rendering item-idref="23" /></region><region region-id="780" left="66" top="1911.75" width="176.25" height="21.75" align-x="117" align-y="1926" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><math optimize="false" export="false" disable-calc="false"><ml:define><ml:apply><ml:matcol /><ml:id subscript="iter">curve</ml:id><ml:id>r</ml:id></ml:apply><ml:apply><ml:id>polyiter</ml:id><ml:id>x</ml:id><ml:id>y</ml:id><ml:apply><ml:plus /><ml:id>r</ml:id><ml:apply><ml:id>min</ml:id><ml:id>x</ml:id></ml:apply></ml:apply><ml:id>N</ml:id><ml:id>ε</ml:id></ml:apply></ml:define></math><rendering item-idref="24" /></region><region region-id="786" left="54" top="1944" width="288.75" height="184.5" align-x="54" align-y="1944" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><plot disable-calc="false" item-idref="25" /><rendering item-idref="26" /></region><region region-id="796" left="0" top="2136" width="6000" height="6" align-x="0" align-y="2136" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><pageBreak /></region><region region-id="792" left="36" top="2150.25" width="334.5" height="36" align-x="36" align-y="2160" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Aitken-Neville iterated interpolation is illustrated in the application worksheet, <b><u><link href="./jupiter.xmcd" title="Links to Application" popup="false">Two-Point, Two-Body Elements for the Planet<sp count="2" />Jupiter</link></u></b>.</p></text></region><region region-id="644" left="36" top="2198.25" width="306.75" height="60" align-x="36" align-y="2208" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The<f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000"> polyint</c></inlineAttr></b></f> and<f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000"> polycoeff </c></inlineAttr></b></f>routines are based on polyint (p.109) and polycoeff (p.121) from the book "Numerical Recipes in C, The Art of Scientific Computing" (Cambridge University Press),<sp count="2" />Copyright (C) 1987, 1988 Numerical Recipes Software, and is used under license. </p></text></region><region region-id="736" left="36" top="2270.25" width="324.75" height="36" align-x="36" align-y="2280" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">polyiter</c></inlineAttr></b></f> routine is described in McCalla, Thomas Richard (1967). <f family="Verdana" charset="0"><i><inlineAttr underline="false" line-through="false"><c val="#000">Introduction to Numerical Methods and FORTRAN Programming</c></inlineAttr></i></f>, John Wiley. </p></text></region><region region-id="733" left="6" top="2334" width="427.5" height="5.25" align-x="6" align-y="2334" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""><png item-idref="27" display-width="435" display-height="3.75" /><rendering item-idref="28" /></region></regions><binaryContent><item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4zMuw6CMBgF4P5tuYoyOf8mLjZh4hmIk4mPQErFW0I0yODb66HgbpvTy9fm
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