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local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="306" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="136" left="24" top="12" width="426" height="15" align-x="42.75" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="14">Пример реализации интерполяционной формулы Лагранжа</f> </text> </region> <region region-id="284" left="18" top="48.75" width="66.75" height="15.75" align-x="68.25" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ORIGIN</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="286" left="18" top="78.75" width="267" height="246.75" align-x="102.75" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">int_lagr</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">xf</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:id xml:space="preserve">length</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">yf</ml:id> <ml:real>0</ml:real> </ml:localDefine> <ml:for> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">p1</ml:id> <ml:real>1</ml:real> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">p2</ml:id> <ml:real>1</ml:real> </ml:localDefine> <ml:for> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:ifThen> <ml:apply> <ml:notEqual/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">p1</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">xf</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">p2</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:localDefine> </ml:program> </ml:ifThen> </ml:for> <ml:localDefine> <ml:id xml:space="preserve">yf</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">yf</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">p1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:for> <ml:id xml:space="preserve">yf</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="289" left="282" top="78.75" width="183" height="14.25" align-x="282" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> - вычисления по формуле Лагранжа </text> </region> <region region-id="290" left="18" top="324.75" width="93.75" height="14.25" align-x="42.75" align-y="336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Исходные данные: </text> </region> <region region-id="279" left="18" top="348.75" width="58.5" height="267.75" align-x="34.5" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">τ</ml:id> <ml:matrix rows="13" cols="1"> <ml:real>0</ml:real> <ml:real>0.7</ml:real> <ml:real>1.4</ml:real> <ml:real>2.1</ml:real> <ml:real>2.8</ml:real> <ml:real>3.5</ml:real> <ml:real>4.2</ml:real> <ml:real>4.9</ml:real> <ml:real>5.6</ml:real> <ml:real>6.3</ml:real> <ml:real>7.0</ml:real> <ml:real>7.7</ml:real> <ml:real>8.4</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="280" left="108" top="348.75" width="68.25" height="267.75" align-x="122.25" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:matrix rows="13" cols="1"> <ml:real>0</ml:real> <ml:real>3.199</ml:real> <ml:real>3.654</ml:real> <ml:real>3.131</ml:real> <ml:real>2.385</ml:real> <ml:real>1.703</ml:real> <ml:real>1.167</ml:real> <ml:real>0.778</ml:real> <ml:real>0.508</ml:real> <ml:real>0.326</ml:real> <ml:real>0.207</ml:real> <ml:real>0.101</ml:real> <ml:real>0.056</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="281" left="210" top="474.75" width="38.25" height="15.75" align-x="225.75" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">n</ml:id> <ml:real>12</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="295" left="18" top="630.75" width="44.25" height="14.25" align-x="39" align-y="642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Расчеты: </text> </region> <region region-id="294" left="18" top="654.75" width="369" height="14.25" align-x="48.75" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> а) вычисление функции в узле точно совпадает с табличным значением: </text> </region> <region region-id="298" left="18" top="678.75" width="117.75" height="20.25" align-x="42" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">cr</ml:id> <ml:apply> <ml:id xml:space="preserve">int_lagr</ml:id> <ml:sequence> <ml:id xml:space="preserve">τ</ml:id> <ml:id xml:space="preserve">c</ml:id> <ml:real>4.2</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="299" left="204" top="678.75" width="66" height="20.25" align-x="226.5" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">cr</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.167</ml:real> </result> 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multiple-assignment="MC11" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="cm"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="306" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="136" left="24" top="12" width="426" height="15" align-x="42.75" align-y="24" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <f size="14">Пример реализации интерполяционной формулы Лагранжа</f> </text> </region> <region region-id="284" left="18" top="48.75" width="66.75" height="15.75" align-x="68.25" align-y="60" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ORIGIN</ml:id> <ml:real>0</ml:real> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="286" left="18" top="78.75" width="267" height="246.75" align-x="102.75" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">int_lagr</ml:id> <ml:boundVars> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">xf</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">n</ml:id> <ml:apply> <ml:id xml:space="preserve">length</ml:id> <ml:id xml:space="preserve">x</ml:id> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">yf</ml:id> <ml:real>0</ml:real> </ml:localDefine> <ml:for> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">p1</ml:id> <ml:real>1</ml:real> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">p2</ml:id> <ml:real>1</ml:real> </ml:localDefine> <ml:for> <ml:id xml:space="preserve">j</ml:id> <ml:range> <ml:real>0</ml:real> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">n</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:range> <ml:ifThen> <ml:apply> <ml:notEqual/> <ml:id xml:space="preserve">j</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:program> <ml:localDefine> <ml:id xml:space="preserve">p1</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">p1</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">xf</ml:id> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:localDefine> <ml:localDefine> <ml:id xml:space="preserve">p2</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">p2</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">x</ml:id> <ml:id xml:space="preserve">j</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:localDefine> </ml:program> </ml:ifThen> </ml:for> <ml:localDefine> <ml:id xml:space="preserve">yf</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve">yf</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">y</ml:id> <ml:id xml:space="preserve">i</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">p1</ml:id> <ml:id xml:space="preserve">p2</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:localDefine> </ml:program> </ml:for> <ml:id xml:space="preserve">yf</ml:id> </ml:program> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="289" left="282" top="78.75" width="183" height="14.25" align-x="282" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> - вычисления по формуле Лагранжа </text> </region> <region region-id="290" left="18" top="324.75" width="93.75" height="14.25" align-x="42.75" align-y="336" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Исходные данные: </text> </region> <region region-id="279" left="18" top="348.75" width="58.5" height="267.75" align-x="34.5" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">τ</ml:id> <ml:matrix rows="13" cols="1"> <ml:real>0</ml:real> <ml:real>0.7</ml:real> <ml:real>1.4</ml:real> <ml:real>2.1</ml:real> <ml:real>2.8</ml:real> <ml:real>3.5</ml:real> <ml:real>4.2</ml:real> <ml:real>4.9</ml:real> <ml:real>5.6</ml:real> <ml:real>6.3</ml:real> <ml:real>7.0</ml:real> <ml:real>7.7</ml:real> <ml:real>8.4</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="280" left="108" top="348.75" width="68.25" height="267.75" align-x="122.25" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">c</ml:id> <ml:matrix rows="13" cols="1"> <ml:real>0</ml:real> <ml:real>3.199</ml:real> <ml:real>3.654</ml:real> <ml:real>3.131</ml:real> <ml:real>2.385</ml:real> <ml:real>1.703</ml:real> <ml:real>1.167</ml:real> <ml:real>0.778</ml:real> <ml:real>0.508</ml:real> <ml:real>0.326</ml:real> <ml:real>0.207</ml:real> <ml:real>0.101</ml:real> <ml:real>0.056</ml:real> </ml:matrix> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="281" left="210" top="474.75" width="38.25" height="15.75" align-x="225.75" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">n</ml:id> <ml:real>12</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="295" left="18" top="630.75" width="44.25" height="14.25" align-x="39" align-y="642" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Расчеты: </text> </region> <region region-id="294" left="18" top="654.75" width="369" height="14.25" align-x="48.75" align-y="666" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> а) вычисление функции в узле точно совпадает с табличным значением: </text> </region> <region region-id="298" left="18" top="678.75" width="117.75" height="20.25" align-x="42" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">cr</ml:id> <ml:apply> <ml:id xml:space="preserve">int_lagr</ml:id> <ml:sequence> <ml:id xml:space="preserve">τ</ml:id> <ml:id xml:space="preserve">c</ml:id> <ml:real>4.2</ml:real> </ml:sequence> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="299" left="204" top="678.75" width="66" height="20.25" align-x="226.5" align-y="690" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1">cr</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1.167</ml:real> </result> </ml:eval> </math> <rendering item-idref="8"/> </region> <region region-id="300" left="18" top="708.75" width="197.25" height="14.25" align-x="48.75" align-y="720" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> а) вычисление функции между узлами: </text> </region> <region region-id="301" left="18" top="732.75" width="117.75" height="20.25" align-x="42" align-y="744" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="2">cr</ml:id> <ml:apply> <ml:id xml:space="preserve">int_lagr</ml:id> <ml:sequence> <ml:id xml:space="preserve">τ</ml:id> <ml:id xml:space="preserve">c</ml:id> <ml:real>6.1</ml:real> </ml:sequence> </ml:apply> 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