草履虫的BLOG-拉格朗日插值算法

拉格朗日插值:根据已知的一些数据,估算一些未知解的一种插值算法
算法介绍:继续找本书看看,比如数值分析...-_-#
有空会继续其他的插值javascript算法实现.评论被关闭,有问题直接email吧
演示::
预览地址:Demo

<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
    <title>拉格朗日插值</title>
      <script type="text/javascript">
        function getPrecision(x){
          return x.toString().split(".")[1].length;  
        }
        
        Number.prototype.floatFormat = function(n){
          return Math.round(this * Math.pow(10, n)) / Math.pow(10, n);
        }
        /*
         * foregone:一个2维数组,比如:
         *   [
         *     [1,2],
         *     [2,4],
         *     [4,9]
         *   ]
         * 表示已知了三个结果,x=1,y=2;x=2,y=4;x=4,y=9
         * x:目的自变量
         * 
         * 返回值:result,插值估算出的结果
         */
        function Lagrange(foregone,x){
          var xIndex = 0;
          var yIndex = 1;
          var n=foregone.length;
          
          //获取精度
          var percision = 0;
          for(var i =0,j=foregone.length,p;i<j;i++){
            p = getPrecision(foregone[i][yIndex]);
            if(p > percision) {
              percision = p;
            }
          }
          
          for(var i=0,w=1;i<n;i++){
            w *= (x - foregone[i][xIndex]);
          }
          for(var k=0,xk,yk,result=0;k<n;k++){
            xk = foregone[k][xIndex];
            yk = foregone[k][yIndex];
            for(var j=0,wk=1;j<n;j++){
              if(j == k){
                continue;
              }
              wk *= (xk - foregone[j][xIndex]);
            }
            result += yk * w /((x - xk)*wk);
          }
          return result.floatFormat(percision);
        }
        
        /*
         * 已知 sin0.32 = 0.314567; sin0.34 = 0.333487; sin0.36 = 0.352274
         * 求 sin0.3367
         */
        var foregone = [[0.32,0.314567],[0.34,0.333487]];  //线性插值
        var foregone2 = [[0.32,0.314567],[0.34,0.333487],[0.36,0.352274]];  //抛物插值
        var x = 0.3367; 
        alert(Lagrange(foregone,x));
        alert(Lagrange(foregone2,x));
      </script>
    </head>
  <body>
    
  </body>
</html>

提示：您可以先修改部分代码再运行 --------------------------------------------------------------------
核心代码:

/*===========================================================
 * 项目:拉格朗日插值算法实现(javascript)
 * 作者:草履虫
 * 时间:2008.5.24
 * 联系:caolvchong@gmail.com
 * 主页:http://cceer.xmu.edu.cn/blog/
 *===========================================================*/