Cubic Spline by utk13453

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									                                                      Cubic Spline Interpolation Example


Overview: Within this workbook we demonstrate the use of the cubic spline interpolation function "Ipola_Inter_CubicSpline"
          Given a tabulated function (defined at 12 points), we use cubic spline method in order to interpolate
          over the whole continuous range.


Tabulated Function:                   Tabulated Function
                                                                                                   Plot of Tabulated Fu
On the right we have the given        x-axis          y-axis
values of the function at the                    1             12
                                                                                14
tabulation points.                               2             10
                                                 3              1               12
These points have been plotted                   4              3
within the chart entitled                        5              5               10
"Plot of Tabulated Function".                    6              2
                                                 7              3                8




                                                                       y-axis
                                                 8              4
                                                                                 6
                                                 9              5
                                                10              6                4
                                                11              7
                                                12              8                2

                                                                                 0
                                                                                      0   2        4



Cubic Spline Interpolation:           Interpolation   Values
                                      Points                                                  Plot of the Cubic Spline I
In the table on our right we have                 1   #NAME?
used the function:                             1.01   #NAME?
                                               1.02   #NAME?                     1
Ipola_Inter_CubicSpline                        1.03   #NAME?                    0.9
                                               1.04   #NAME?                    0.8
in order to interpolation the given            1.05   #NAME?                    0.7
yabulated function about the                   1.06   #NAME?
tabulation points.                             1.07   #NAME?                    0.6
                                                                       y-axis




                                               1.08   #NAME?                    0.5
We then plot these results                     1.09   #NAME?                    0.4
within the table entitled                       1.1   #NAME?
                                                                                0.3
"Plot of the Cubic Spline                      1.11   #NAME?
Interpolation".                                1.12   #NAME?                    0.2
                                               1.13   #NAME?                    0.1
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 9.55   #NAME?
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 9.57   #NAME?
 9.58   #NAME?
 9.59   #NAME?
  9.6   #NAME?
 9.61   #NAME?
 9.62   #NAME?
 9.63   #NAME?
 9.64   #NAME?
 9.65   #NAME?
 9.66   #NAME?
 9.67   #NAME?
 9.68   #NAME?
 9.69   #NAME?
  9.7   #NAME?
 9.71   #NAME?
 9.72   #NAME?
 9.73   #NAME?
 9.74   #NAME?
 9.75   #NAME?
 9.76   #NAME?
 9.77   #NAME?
 9.78   #NAME?
 9.79   #NAME?
  9.8   #NAME?
 9.81   #NAME?
 9.82   #NAME?
 9.83   #NAME?
 9.84   #NAME?
 9.85   #NAME?
 9.86   #NAME?
 9.87   #NAME?
 9.88   #NAME?
 9.89   #NAME?
  9.9   #NAME?
 9.91   #NAME?
 9.92   #NAME?
 9.93   #NAME?
 9.94   #NAME?
 9.95   #NAME?
 9.96   #NAME?
 9.97   #NAME?
 9.98   #NAME?
 9.99   #NAME?
   10   #NAME?
10.01   #NAME?
10.02   #NAME?
10.03   #NAME?
10.04   #NAME?
10.05   #NAME?
10.06   #NAME?
10.07   #NAME?
10.08   #NAME?
10.09   #NAME?
 10.1   #NAME?
10.11   #NAME?
10.12   #NAME?
10.13   #NAME?
10.14   #NAME?
10.15   #NAME?
10.16   #NAME?
10.17   #NAME?
10.18   #NAME?
10.19   #NAME?
 10.2   #NAME?
10.21   #NAME?
10.22   #NAME?
10.23   #NAME?
10.24   #NAME?
10.25   #NAME?
10.26   #NAME?
10.27   #NAME?
10.28   #NAME?
10.29   #NAME?
 10.3   #NAME?
10.31   #NAME?
10.32   #NAME?
10.33   #NAME?
10.34   #NAME?
10.35   #NAME?
10.36   #NAME?
10.37   #NAME?
10.38   #NAME?
10.39   #NAME?
 10.4   #NAME?
10.41   #NAME?
10.42   #NAME?
10.43   #NAME?
10.44   #NAME?
10.45   #NAME?
10.46   #NAME?
10.47   #NAME?
10.48   #NAME?
10.49   #NAME?
 10.5   #NAME?
10.51   #NAME?
10.52   #NAME?
10.53   #NAME?
10.54   #NAME?
10.55   #NAME?
10.56   #NAME?
10.57   #NAME?
10.58   #NAME?
10.59   #NAME?
 10.6   #NAME?
10.61   #NAME?
10.62   #NAME?
10.63   #NAME?
10.64   #NAME?
10.65   #NAME?
10.66   #NAME?
10.67   #NAME?
10.68   #NAME?
10.69   #NAME?
 10.7   #NAME?
10.71   #NAME?
10.72   #NAME?
10.73   #NAME?
10.74   #NAME?
10.75   #NAME?
10.76   #NAME?
10.77   #NAME?
10.78   #NAME?
10.79   #NAME?
 10.8   #NAME?
10.81   #NAME?
10.82   #NAME?
10.83   #NAME?
10.84   #NAME?
10.85   #NAME?
10.86   #NAME?
10.87   #NAME?
10.88   #NAME?
10.89   #NAME?
 10.9   #NAME?
10.91   #NAME?
10.92   #NAME?
10.93   #NAME?
10.94   #NAME?
10.95   #NAME?
10.96   #NAME?
10.97   #NAME?
10.98   #NAME?
10.99   #NAME?
   11   #NAME?
11.01   #NAME?
11.02   #NAME?
11.03   #NAME?
11.04   #NAME?
11.05   #NAME?
11.06   #NAME?
11.07   #NAME?
11.08   #NAME?
11.09   #NAME?
 11.1   #NAME?
11.11   #NAME?
11.12   #NAME?
11.13   #NAME?
11.14   #NAME?
11.15   #NAME?
11.16   #NAME?
11.17   #NAME?
11.18   #NAME?
11.19   #NAME?
 11.2   #NAME?
11.21   #NAME?
11.22   #NAME?
11.23   #NAME?
11.24   #NAME?
11.25   #NAME?
11.26   #NAME?
11.27   #NAME?
11.28   #NAME?
11.29   #NAME?
 11.3   #NAME?
11.31   #NAME?
11.32   #NAME?
11.33   #NAME?
11.34   #NAME?
11.35   #NAME?
11.36   #NAME?
11.37   #NAME?
11.38   #NAME?
11.39   #NAME?
 11.4   #NAME?
11.41   #NAME?
11.42   #NAME?
11.43   #NAME?
11.44   #NAME?
11.45   #NAME?
11.46   #NAME?
11.47   #NAME?
11.48   #NAME?
11.49   #NAME?
 11.5   #NAME?
11.51   #NAME?
11.52   #NAME?
11.53   #NAME?
11.54   #NAME?
11.55   #NAME?
11.56   #NAME?
11.57   #NAME?
11.58   #NAME?
11.59   #NAME?
 11.6   #NAME?
11.61   #NAME?
11.62   #NAME?
11.63   #NAME?
11.64   #NAME?
11.65   #NAME?
11.66   #NAME?
11.67   #NAME?
11.68   #NAME?
11.69   #NAME?
 11.7   #NAME?
11.71   #NAME?
11.72   #NAME?
11.73   #NAME?
11.74   #NAME?
11.75   #NAME?
11.76   #NAME?
11.77   #NAME?
11.78   #NAME?
11.79   #NAME?
 11.8   #NAME?
11.81   #NAME?
11.82   #NAME?
11.83   #NAME?
11.84   #NAME?
11.85   #NAME?
11.86   #NAME?
11.87   #NAME?
11.88   #NAME?
11.89   #NAME?
 11.9   #NAME?
11.91   #NAME?
11.92   #NAME?
11.93   #NAME?
11.94   #NAME?
11.95   #NAME?
11.96   #NAME?
11.97   #NAME?
11.98   #NAME?
11.99   #NAME?
   12   #NAME?
 ction "Ipola_Inter_CubicSpline"
order to interpolate




        Plot of Tabulated Function




                                                        Tab.Pts




                 6             8   10   12     14
                      x-axis



 Plot of the Cubic Spline Interpolation




                  6            8   10   12      14
                      x-axis                 Cubic interpolation

								
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