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 `@ -31,6 +31,27 @@` ``` ``` `; Thiele's interpolation formula` `; ==============================` `; ` `; In the following example, we use Thiele's interpolation formula` `; for computing the inverse cos function cos^(-1) from 32 points` `; given by the cos function itself.` `; ` `; We create two vectors:` `; * the vector 'a' contains regularly spaced points in [0..1.55]` `; * the vector 'b' contains cos(x) for each x in vector 'a'` `; ` `; We set the keepfloat flag to true in order to prevent Maxima` `; to replace the values with rational approximations.` `; ` `; Then we compute the inverse function by using thiele(b,a);` `; we evaluate this interpolation at 0.5 expecting some value` `; close to pi/3.` `; ` `; (%i1) a:makelist(0.05*i,i,0,31)\$` `; (%i2) b:makelist(float(cos(0.05*i)),i,0,31)\$` `; (%i3) keepfloat:true\$` `; (%i4) subst(x=0.5, thiele(b,a))*3;` `; (%o4) 3.14159265357928` ``` ``` `(defun \$thiele (u v)` ` (loop for rh on`