Implementation of Lagrange interpolation method in Java

definition of Lagrange interpolation method (quoted from Wikipedia)

For a polynomial function, it is known that there is a given K + 1 value point:

( x0,y0), (X1,y1), (x2,y2),??, (Xk,yk)

where XJ corresponds to the position of the argument, and YJ corresponds to the value of the function at that position.

Assuming that any two different x-J are not the same, then the Lagrangian interpolation polynomial obtained by the Lagrange interpolation formula is:

Each of these is a lagrand-day basic polynomial (or interpolation-based function ) whose expression is:

The specific Java code:

1 ImportJava.util.Scanner;2 3 4  Public classLagrange {5     Private Static Double[] Lag (DoubleX[],DoubleY[],Doublex0[]) {6         intm=x.length;7         intn=x0.length;8         Doubley0[]=New Double[n];9          for(intia=0;ia<n;ia++) {Ten             DoubleJ=0; One              for(intib=0;ib<m;ib++) { A                 DoubleK=1; -                  for(intIc=0;ic<m;ic++) { -                     if(ib!=IC) { theK=k* (X0[ia]-x[ic])/(x[ib]-X[ic]); -                     } -                 } -k=k*Y[ib]; +j=j+K; -             } +y0[ia]=J; A         } at         returny0; -     } -      Public Static voidMain (string[] args) { -System.out.println ("Please enter the number of interpolated points given:"); -Scanner input=NewScanner (system.in); -         intm=input.nextint (); inSystem.out.println ("Please enter the number of interpolated points for the demand solution:"); -         intn=input.nextint (); to         Doublex[]=New Double[m]; +         Doubley[]=New Double[m]; -         Doublex0[]=New Double[n]; theSystem.out.println ("Enter the given interpolation point in turn:"); *          for(inti=0;i<m;i++){ $x[i]=input.nextdouble ();Panax Notoginseng         } -System.out.println ("Enter the function value corresponding to the given interpolation point in turn:"); the          for(inti=0;i<m;i++){ +y[i]=input.nextdouble (); A         } theSystem.out.println ("Enter the interpolation point of the demand solution in turn"); +          for(inti=0;i<n;i++){ -x0[i]=input.nextdouble (); $         } $         Doubley0[]=Lag (x, y, x0); -System.out.println ("Using Lagrange interpolation method to solve:"); -          for(inti=0;i<n;i++){ theSystem.out.println (y0[i]+ ""); -         }Wuyi System.out.println (); the input.close (); -     } Wu}

Code

The disadvantage of Lagrange interpolation method is that the calculated result is unstable when the interpolation point is more, and can be improved by defining a weight of center of gravity, the improved interpolation method is generally called the centroid Lagrange interpolation method.

Implementation of Lagrange interpolation method in Java