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Das Heronverfahren

Berechnen der Quadratwurzel von a

a =
k0 =

i ki ki2

// Das Heronverfahren (c)2007 dh

var
i = 0;
var j = 0;

function Add0(zahlstr) {
/* sorgt für eine formatierte Ausgabe der Zahlenwerte */

   var input = zahlstr;
   var dot = false;
   var pos = 0;

   for (j = 0; j <= input.length; j++) {
      if (input.charCodeAt(j) == 46) {dot = true; pos = j}
   }

   var st = "";
   if (dot == true) {
      var n0 = 11 - input.length + pos;
      for (j = 1; j <= n0; j++) {st = st + "0"}
   }
   else {
      input = input + ".";
      for (j = 0; j <= input.length; j++) {
         if (input.charCodeAt(j) == 46) pos = j
   }

   st = "";
   var n0 = 11 - input.length + pos;
   for (j = 1; j <= n0; j++) {st = st + "0"}
   }
   return input + st;
}

function CheckInput(inp) {
/* findet fehlerhafte Eingaben */

   var input = inp;
   var key;
   var value = "";
   var noValue = false;
   var isDot = false;

   for (j = 0; j < input.length; j++) {
      key = input.charCodeAt(j);
      if ((key < 48)||(key > 57)) {
         if ((key == 44)||(key == 46)) {
            value = value + ".";
            if (!isDot) {isDot = true} else {noValue = true}
         }
         else {noValue = true}
      }
      else {value = value + String.fromCharCode(key)}
   }
   if ((noValue)||(value == ".")||(value == "0")) {value = ""}
   return value;
}

function Heron() {
/* berechnet näherungsweise die Quadratwurzel aus a */

   var inp_k0 = CheckInput(document.f_startwert.e_k0.value);
   var inp_a = CheckInput(document.f_startwert.e_a.value);
   if ((inp_a == "")||(inp_k0 == "")) {
      document.f_startwert.e_k0.value = "";
      document.f_startwert.e_a.value = "";
   }
   else {
      document.f_startwert.e_k0.value = inp_k0;
      document.f_startwert.e_a.value = inp_a;

      var kOld = 1*inp_k0;
      var a = 1*inp_a;

      var d = 1;
      var h = 0;
      var kNew = 0;

      j = i;
      while (j > 0) {
         document.getElementById("Tabelle").deleteRow(j);
         j--;
      }

      i = 0;
      styleValue = "text−align:right; border:1px solid #04027B; height:16px";

      while ((d > 0.0000000001)&&(i < 20)) {
         var row = document.getElementById("Tabelle").insertRow(i+1);
         h = a/kOld;           
         kNew = 0.5*(kOld + h);
         d = Math.abs(kNew - kOld);

         var td1 = document.createElement("td");
         td1.setAttribute ("style", styleValue);
         var td1Text = i;
         var td1Node = document.createTextNode(td1Text);
         td1.appendChild(td1Node);

         var td2 = document.createElement("td");
         td2.setAttribute ("style", styleValue);
         var pow = 10000000000;
         var td2Text = Add0("" + Math.round(kOld*pow)/pow);
         var td2Node = document.createTextNode(td2Text);
         td2.appendChild(td2Node);

         var td3 = document.createElement("td");
         td3.setAttribute ("style", styleValue);
         var td3Text = Add0("" + Math.round(kOld*kOld*pow)/pow);
         var td3Node = document.createTextNode(td3Text);
         td3.appendChild(td3Node);

         row.appendChild(td1);
         row.appendChild(td2);
         row.appendChild(td3);

         i += 1;
         kOld = kNew;
      }
   }
}

Das Heronverfahren


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