Example: Cubic Splines with Known Derivatives
The example for Cubic Splines with Known Data Points produced the second derivatives at each entered point. The following example uses those derivatives to arrive at the same result
Example
From the second derivatives listed below, interpolate the function at 0.8.|
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x |
f''(x) |
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| 0.6 | -0.1999347 |
| 0.7 | -0.2200526828 |
| 0.9 | -0.2409746016 |
| 1.0 | -0.2422470246 |
| 1.1 | -0.2396373 |
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Procedure |
Press |
Display |
|---|---|---|
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| Select the program | [ RUN ] { MTH } { INT } { CUB } { NEW } |
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| Enter the number of points | 5 { m } { EOD } |
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| Enter second derivatives | .1999347 [ +/- ] { ENT } |
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| .2200526828 [ +/- ] { ENT } |
 |
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| .2409746016 [ +/- ] { ENT } |
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| .2422470246 [ +/- ] { ENT } |
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| .2396373 [ +/- ] { ENT } |
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| Interpolate at .8 | { NO } .8 { x } |
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| Repeat the problem | { ESC } { ESC } { OLD } |
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Procedure |
Press |
Display |
|---|---|---|
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| Enter the number of points | 5 { m } { EOD } |
 |
| Enter second derivatives | 0 { ENT } |
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| [ CE ] { ENT } |
 |
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| [ CE ] { ENT } |
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| [ CE ] { ENT } |
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| 0 { ENT } |
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| Interpolate at .8 | { NO } .8 { x } |
 |
The result is the same as for nonzero endpoint second derivatives. The endpoints are too distant from the point of interpolation for a small change in the endpoint second derivative to have any effect on the result.
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