Newton interpolation polynomial

1 //Topic Requirements:interpolation using Newton's difference quotient formula2#include <iostream>3#include <cmath>4#include <cstring>5 using namespacestd;6 #defineNUMOFX 20//define the size of the data volume7 structdata{8     Doublex;9     DoubleFx//defines the point at which the operation is performed (X,FX)Ten }POINTDATA[NUMOFX]; One  A //the formula of finding the difference quotient F (X0,X1,X2...XN) - Long DoubleChashang (intN) {//calculation F[x0,x1,x2...xn] -     if(n<=0){ the         return 0; -     } -      -     Long Doubleresult=0; +      for(intI=0; i<=n;i++){ -         //calculate the 0~n of the computed value of this +         Long Doubleresproduct=1; A          for(intj=0; j<=n;j++){ at             if(j!=i) { -Resproduct*= (pointdata[i].x-pointdata[j].x);  -             }               -         }  -         Long Doubletemp=pointdata[i].fx/resproduct; -result+=temp; in     } -     returnresult; to }  +                         - intMain () { the     intNumofpoint; *cout<<"The number of interpolated points that will be entered is:"; $Cin>>Numofpoint;Panax Notoginsengcout<<"Please enter the value of X,FX: \ n";  -      for(intI=0; i<numofpoint;i++){ theCin>>pointdata[i].x>>pointdata[i].fx; +     } A      the     //Print output Newton difference quotient formula, not simple +cout<<"The Newton interpolation polynomial calculated from the above interpolation points is: \ n";  -cout<<"f (x) ="<<pointdata[0].fx; $      for(intI=1; i<numofpoint;i++){ $         Long Doubletemp4=Chashang (i); -         if(temp4>=0){ -cout<<"+"<<temp4<<"*"; the         } -         Else{Wuyicout<<temp4<<"*"; the         } -          Wu          for(intj=0; j<i;j++){ -cout<<"(X-"<<pointdata[j].x<<")"; About         } $     }  -      -     //calculate Newton interpolation polynomial approximation of an x -     Doublex; Acout<<"\ n \ nyou Enter the value of the variable x to be evaluated:"; +Cin>>x; thecout<<"The approximate result of Newton interpolation polynomial is:"; -       $     Long Doubleres=pointdata[0].fx;//the F (x0) term of Newton's difference quotient formula the      for(intI=0; i<numofpoint-1; i++) {//Newton interpolation polynomial term f[x0,x1...xn] (x-x0) (x-x1) ... (X-XN) N>=1 the  the         Long Doubletemp=1; the          for(intj=0; j<=i;j++){ -temp=temp* (xpointdata[j].x);  in         } the          theRes=res+chashang (i+1)*temp; About     } thecout<<res<<Endl; the}

Lagrange Interpolation procedure:

1#include <iostream>2#include <fstream>3 using namespacestd;4 5 classlagrange{6 7     Private:8         intI,j,n;9         Doublemult,sum,z;Ten         Double*x,*y; One          A      Public: -         voidinterpolation () { -Ifstream Fin ("a.txt"); theFin>>N; -x=New Double[n]; -y=New Double[n]; -              for(i=0; i<n;i++){ +Fin>>x[i]>>Y[i]; -             } + fin.close (); Acout<<"\ n Enter the points that need to be interpolated:"; atCin>>Z; -sum=0.0; -              -              for(i=0; i<n;i++){ -mult=1.0; -                  for(j=0; j<n;j++){ in                     if(j!=i) { -Mult*= (Z-x[j])/(x[i]-x[j]); to                     }  +                 } -sum+=mult*Y[i]; the             }  *cout<<"\ n interpolated value ="<<sum<<Endl; $                         Panax Notoginseng         } -          the~Lagrange () { +             Delete[] x, y; A         } the      + }; -  $ intMain () { $ Lagrange Interp; - interp.interpolation (); -}

Newton interpolation polynomial