Hermite 插值多项式——JAVA实现

╰+攻爆jí腚メ 2022-02-25 13:30 409阅读 0赞

# Hermite 插值多项式计算近似值——JAVA实现 #

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import java.util.Scanner;
    public class Hermite {
    	//x x //y y //m m // x0 插入的值   // y0 近似值
    
    	public static double[] aaa(double x[],double y[], double m[], double x0[]) {
    			int a=x.length;
    			int b=x0.length;
    			double y0[]=new double[b];
    			double add_xj_xk=0;//连加
    			double mul_x0_xk=1;//连乘
    			double add_h2n1x=0;//近似值
    			
    		
    			for (int i=0;i<b;i++) {//一重循环将不同插值点近似值传给数组y0
    				add_h2n1x=0;
    				for (int j=0;j<a;j++) {//二重循环计算H2n+1(x)
    					mul_x0_xk=1;
    					add_xj_xk=0;
    						for(int k=0;k<a;k++) {//三重循环计算l'j(xj)和lj(x)
    						if (j!=k) {				
    							add_xj_xk+=1/(x[j]-x[k]);
    							mul_x0_xk*=((x0[i]-x[k])/(x[k]-x[j]));
    							
    						}
    					}
    				
    					add_h2n1x+=(y[j]*(1-(2*(x0[i]-x[j])*add_xj_xk))*(mul_x0_xk*mul_x0_xk))+(m[j]*(x0[i]-x[j])*(mul_x0_xk*mul_x0_xk));
    					
    		
    				}
    				
    				y0[i]=add_h2n1x;
    				
    			}
    		
    		
    		return y0;
    	}
    	public static void main(String[] args) {
    		double []x= {0.10,0.20,0.30,0.40,0.50,0.60,0.70,0.80,0.90,1.00};
    		double []y= {0.904837,0.818731,0.740818,0.670320,0.606531,0.548812,0.496585,0.449329,0.406570,0.367879};
    		double []m= {-0.904837,-0.818731,-0.740818,-0.670320,-0.606531,-0.548812,-0.496585,-0.449329,-0.406570,-0.367879};
    		System.out.println("输入插值点个数：");
    		Scanner scan =new Scanner(System.in);
    		int n=scan.nextInt();
    		double X0[]=new double[n];
    		System.out.println("输入插值点横坐标：");//需要求的插值点的横坐标标值
            for(int i=0;i<n;i++){
                X0[i]=scan.nextDouble();
            }
             
            double Y0[]=aaa(x, y, m, X0);//使用H插值法求解得到需求插值点的纵坐标值
            System.out.println("H插值法求解得:");
            for(int i=0;i<n;i++){
                System.out.println(Y0[i]+" ");
            }
            System.out.println();
    
    		
    	}
    
    }