Numerical Analysis Programs Using Fortran 90 - University of ...

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Problem: Write a program to find the interpolated value for x = 3, using Lagrangian Polynomial, from the following data. X 3.2 2.7 1 4.8 F(x) 22 17.8 14.2 38.3 program Lagrange_Iterpolation dimension x(20),y(20) n=4 xx=3 data (x(i), i=1,4)/3.2,2.7,1,4.8/ data (y(i), i=1,4)/22,17.8,14.2,38.3/ s=0 do i=1,n p=1 do j=1,n if (i.eq.j) goto 5 p=p*(xx-x(j))/(x(i)-x(j)) 5 enddo s=s+p*y(i) enddo print*,'Interpolation <strong>of</strong>(',xx,')=',s end ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Interpolation <strong>of</strong> (3) = 20.21196 22
Problem: Write a program to determine the parameters a 1 & a 2 so that ( x) = a + a x , fits the following data in least squares sense. f 1 2 X 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 y 1 2.7 4.3 6 7.5 9 10.6 12 program List_Square_Fitting dimension x(20),y(20),f(20) n=8 data (x(i), i=1,8)/0,.3,.6,.9,1.2,1.5,1.8,2.1/ data (y(i), i=1,8)/1,2.7,4.3,6,7.5,9,10.6,12/ sx=0; sxx=0;sy=0;sxy=0 do i=1,n sx=sx+x(i) sy=sy+y(i) sxx=sxx+x(i)**2 sxy=sxy+x(i)*y(i) enddo print *,'sx=',sx print *,'sxx=',sxx print *,'sy=',sy print *,'sxy=',sxy d=n*sxx-sx**2 a1=(sxx*sy-sx*sxy)/d a2=(n*sxy-sx*sy)/d print*,'a1=',a1 print*,'a2=',a2 s=0 do i=1,n f(i)=a1+a2*x(i) s=s+(y(i)-f(i))**2 enddo print*,'Standerd Deviation=',s end ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ sx=8.4 sxx=12.6 sy=53.1 sxy=75.57 a1=1.133333 a2=5.242064 Standard deviation = 6.726178 E -02 23
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Numerical Analysis Programs Using Fortran 90 - University of ...

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