Data update

Task/Steffensens-method/ALGOL-68/steffensens-method.alg

@@ -46,7 +46,7 @@ BEGIN # Steffenses's method - translated from the ATS sample #
 
     PROC implicit equation = ( REAL x, y )REAL: ( 5 * x * x ) + y - 5;
 
-    PROC f = ( REAL t )REAL: # find fixed points of this function #
+    PROC fn = ( REAL t )REAL: # find fixed points of this function #
          BEGIN
             REAL x = x convex left parabola( t );
             REAL y = y convex left parabola( t );
@@ -60,7 +60,7 @@ BEGIN # Steffenses's method - translated from the ATS sample #
         REAL t0 := 0;
         TO 11 DO
             print( ( "t0 = ", FMT t0, " : " ) );
-            CASE steffensen aitken( f, t0, 0.00000001, 1000 )
+            CASE steffensen aitken( fn, t0, 0.00000001, 1000 )
               IN ( VOID   ): print( ( "no answer", newline) )
                , ( REAL t ):
                      IF REAL x = x convex left parabola( t )

Task/Steffensens-method/C++/steffensens-method.cpp

@@ -56,7 +56,7 @@ int main() {
         cout << "t0 = " << setprecision(1) << t0 << " : ";
         t = steffensenAitken(f, t0, 0.00000001, 1000);
         if (isnan(t)) {
-            cout << "no answer << endl;
+            cout << "no answer" << endl;
         } else {
             x = xConvexLeftParabola(t);
             y = yConvexRightParabola(t);

Task/Steffensens-method/Perl/steffensens-method.pl

@@ -0,0 +1,63 @@
+# 20240922 Perl programming solution
+
+use strict;
+use warnings;
+sub aitken {
+   my ($f, $p0) = @_;
+   my $p2 = $f->( my $p1 = $f->($p0) );
+   return $p0 - ($p1 - $p0)**2 / ($p2 - 2 * $p1 + $p0);
+}
+
+sub steffensenAitken {
+   my ($f, $pinit, $tol, $maxiter) = @_;
+   my ($iter,$p) = (1, aitken($f, my $p0 = $pinit) );
+
+   while (abs($p - $p0) > $tol && $iter < $maxiter) {
+      $p = aitken($f, $p0 = $p);
+      $iter++
+   }
+   return abs($p - $p0) > $tol ? 'NaN' : $p;
+}
+
+sub deCasteljau {
+   my ($c0, $c1, $c2, $t) = @_;
+   my $s = 1.0 - $t;
+   return $s * ($s * $c0 + $t * $c1) + $t * ($s * $c1 + $t * $c2);
+}
+
+sub xConvexLeftParabola {
+   my ($t) = @_;
+   return deCasteljau(2.0, -8.0, 2.0, $t);
+}
+
+sub yConvexRightParabola {
+   my ($t) = @_;
+   return deCasteljau(1.0, 2.0, 3.0, $t);
+}
+
+sub implicitEquation {
+   my ($x, $y) = @_;
+   return 5.0 * ($x ** 2) + $y - 5.0;
+}
+
+sub f {
+   my ($t) = @_;
+   return implicitEquation(xConvexLeftParabola($t), yConvexRightParabola($t)) + $t;
+}
+
+for (my $t0 = 0.0, my $i = 0; $i < 11; ++$i) {
+   printf("t0 = %.1f : ", $t0);
+   my $t = steffensenAitken(\&f, $t0, 1e-8, 1000);
+
+   if ($t eq 'NaN') {
+      print "no answer\n";
+   } else {
+      my ($x, $y) = (xConvexLeftParabola($t), yConvexRightParabola($t));
+      if (abs(implicitEquation($x, $y)) <= 1e-6) {
+         printf("intersection at (%f, %f)\n", $x, $y);
+      } else {
+         print "spurious solution\n";
+      }
+   }
+   $t0 += 0.1;
+}