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NewtonRaphson breakdown
The file attached shows the results of using a spline curve that seems to breakdown over a certain region. Can anyone tell me why that region is so special and why using the NewtonRaphson method could yield these results?
Columns A and B represent the (x,y) data for a calibration curve. See plot of spline curve. The curve is generated by calculating y = ax^3 + bx^2 +cx + d, where the spline coefficients a, b, c, and d are used over certain regions (colorcoded for clarity). For example, for x = 0 to 100, use the 1st row of coefficients, for x = 100 to 500, use the 2nd row, etc.
Columns E anf F represent the actual calibration (x,y) data that are used to generate the spline coefficients in Columns J through M.
Column C represents the values for x when using the NewtonRaphson method for the corresponding y value. Notice that everything is fine up until x =364. From x = 372 to x = 500, the NewtonRaphson method "blow up". For values greater than x = 500 the NewtonRaphson method is normal.
So, what causes the "blowup. What is so special about those particular values of y using the appropriate set of coefficients?
Thanks for any insight as this is driving me crazy.