# runge1.r          Observe Runge phenomenon with interpolation
 #
  npts = 100                        # points for plotting
  for ( n in(c(5,7,9))) {           # how many points for interpolation
   xi <- 4*(2*(1:n)-n-1)/(n-1)      # equally spaced interpolation pts    
   b <- 1/(1+xi*xi)                 # function values
   A <- outer(xi,(0:(n-1)),FUN="^") # vandermonde matrix
   print(A)
   b <- solve(A,b)                  # solution
 # now get ready to plot
   x <- 4.1*(2*(1:npts)-npts-1)/(npts-1)
   s <- 1/(1+x*x)                   # true function
   y <- outer(x,(0:(n-1)),FUN="^") %*% b          # interpolated values
   print(cbind(x,s,y))
   plot(c(x,x),c(s,y))              # Figure 7.1
                      }
  rm(list=ls())
  q()