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Interpolation
Interpolation is a technique to find the value of a dependent variable on the basis of a given set of data or both the variables. In other words on the basis of given set of date (xi,yi) for I=0,1,2,3 ………n, the tachnique to find y for any given value x is called interpolation or extrapolation. These two terms differ only in concept. If x0 A number of technique have been defined in Numerical Analysis for interpolation or extrapolation.
Fortran Program for Interpolation :
C PROGRAM FOR NEWTON FORMULA FOR INTERPOLATION
INTEGER N
REAL XP,FP,SUM,PI,X,F,A,D
DIMENSION X(10),F(10),A(10),D(10,10)
WRITE(*,*)'INPUT NUMBER OF DATA POINTS'
READ(*,*) N
WRITE(*,*)'INPUT VALUE OF X AND F(X) ONE SET ON EACH LINE'
DO 10 I=1,N
READ(*,*) X(I),F(I)
10 CONTINUE
C CONSTRUCT DIFFERENCE TABLE D
DO 20 I=1,N
D(I,1)=F(I)
20 CONTINUE
DO 40 J=2,N
DO 30 I=1,N-J+1
D(I,J)=(D(I+1,J-1)-D(I,J-1))/(X(I+J-1)-X(I))
30 CONTINUE
40 CONTINUE
C SET THE COEFFICIENT OF INTERPOLATING POLYNOMIAL
DO 50 J=1,N
A(J)=D(1,J)
50 CONTINUE
C COMPUTE INTERPOLATION VALUE
WRITE(*,*)'INPUT XP WHERE INTERPOLATION IS REQUIRED'
READ(*,*) XP
SUM=A(1)
DO 70 I=2,N
PI=1.0
DO 60 J=1,I-1
PI=PI*(XP-X(J))
60 CONTINUE
SUM=SUM+A(I)*PI
70 CONTINUE
FP=SUM
C WRITE RESULT
WRITE(*,*)
WRITE(*,*) 'NEWTON INTERPOLATION'
WRITE(*,*)
WRITE(*,*)'Interpolated Function Value'
WRITE(*,*) 'at X=',XP,'is',FP
WRITE(*,*)
STOP
END
OUTPUT:
INTERPOLATION
NEWTON FORMULA
D:\FORTRAN\BINB>NWTINT
INPUT NUMBER OF DATA POINTS
3
INPUT VALUE OF X AND F(X) ONE SET ON EACH LINE
2 1.4142
3 1.7321
4 2.0
INPUT XP WHERE INTERPOLATION IS REQUIRED
2.5
NEWTON INTERPOLATION
Interpolated Function Value
at X= 2.500000is 1.579400
Stop - Program terminated.
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