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chapter iv. runge example, with cubic hermite interpolation
c from * a practical guide to splines * by c. de boor
integer i,istep,j,n,nm1
real aloger,algerp,c(4,20),decay,divdf1,divdf3,dtau,dx,errmax,g,h
* ,pnatx,step,tau(20),x
data step, istep /20., 20/
g(x) = 1./(1.+(5.*x)**2)
print 600
600 format(28h n max.error decay exp.//)
decay = 0.
do 40 n=2,20,2
c choose interpolation points tau(1), ..., tau(n) , equally
c spaced in (-1,1), and set c(1,i) = g(tau(i)), c(2,i) =
c gprime(tau(i)) = -50.*tau(i)*g(tau(i))**2, i=1,...,n.
nm1 = n-1
h = 2./float(nm1)
do 10 i=1,n
tau(i) = float(i-1)*h - 1.
c(1,i) = g(tau(i))
10 c(2,i) = -50.*tau(i)*c(1,i)**2
c calculate the coefficients of the polynomial pieces
c
do 20 i=1,nm1
dtau = tau(i+1) - tau(i)
divdf1 = (c(1,i+1) - c(1,i))/dtau
divdf3 = c(2,i) + c(2,i+1) - 2.*divdf1
c(3,i) = (divdf1 - c(2,i) - divdf3)/dtau
20 c(4,i) = (divdf3/dtau)/dtau
c
c estimate max.interpolation error on (-1,1).
errmax = 0.
do 30 i=2,n
dx = (tau(i)-tau(i-1))/step
do 30 j=1,istep
h = float(j)*dx
c evaluate (i-1)st cubic piece
c
pnatx = c(1,i-1)+h*(c(2,i-1)+h*(c(3,i-1)+h*c(4,i-1)))
c
30 errmax = amax1(errmax,abs(g(tau(i-1)+h)-pnatx))
aloger = alog(errmax)
if (n .gt. 2) decay =
* (aloger - algerp)/alog(float(n)/float(n-2))
algerp = aloger
40 print 640,n,errmax,decay
640 format(i3,e12.4,f11.2)
stop
end
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