Bracket Bli

A function can have a spike at an unkown location.

Figure 1 Tan(x)-137

            The 40 points are logarithmically placed around the starting point of p/2.  Note that this point gave 1.6 x 10¹⁶.  There was no point found less than zero, so the code reported that it could not solve the equation.  This is not acceptable.

            The 20 logarithmically spaced points in the code for\BRACK.FOR could simply miss the peak, or there might be no peak. 

Bli

            The Best Linear Interpolator is designed to give a file containing x, and y values on a variable mesh giving the best picture of the function.  Directions to the bli code are given at the beginning of ..\interpolation\Bli.doc.  The general idea is to use the bli to completely map the function after the original search has failed to find f1´f2 < 0.  The code is in brackbli.zip.

Figure 2 Output from brackbli on failure.

            This is the file fail.out.  It is produced when

Tan(x)- 13777798537 ß 1.38´10¹⁰ is solved for.  The bli part has the **8 in the range changed to **2.  As can be seen above, the tan has a value on the other side of p/2 which makes for easy plotting.  The x that solves this is nearly p/2 which confuses the code a bit.  The Fortran code is brackbli.for in