Thread: Failure of a spline curve

Hi:

This is my first post, so forgive me if this is not the right forum. Please direct to correct forum, if necessary

I've done many spline calculations but the data below yields some strange results.

Table 1 represents the x,y data that is used to create the spline.
Table 2 represents the spline coefficients.

To determine x for a certain value of y I use the Newton-Raphson method.

The question is why for the value of y = 0.16721 does the value of x calculate to 770.35 when clearly it should be around 500.

Yet, when y = 0.16740, x = 500.58. That makes sense.

Also, why for a value of y = 0.14788 does the value of x calculate to -238.97. Based on the x,y data, x should be around 375, not a negative number.

Doesn't make sense to me.


Table 1
x y
1E-20 0.09215762
100 0.098262815
500 0.167314111
750 0.187933238
1000 0.198293337

Table 2
ai bi ci di
1.57803E-09 0 4.52716E-05 0.09215762
-6.83425E-10 4.73409E-07 9.26125E-05 0.098262815
4.1369E-10 -3.467E-07 0.000143296 0.167314111
4.85776E-11 -3.64332E-08 4.75126E-05 0.187933238
0 0 0 0

Thanks for any help in this matter.

You can always double check the spline equations by plugging in the boundary conditions (they should give you the exact values for x and y). Doing a quick check (I may have typed some numbers incorrectly), it seems like you last spline equation does not compute correctly at the boundaries y(750) = .2235? Double check this.

Also, since the spline is piecewise, make sure you are evaluating with the correct piece for a particular value of x when using Newton-Raphson. Also, since it is cubic, there may be multiple solutions for a single y. If you start with an initial guess closer to the expected solution, then you are more likely to get that solution.