Fixed Point Iteration

---

Function g(x)

g <- function(x) {
    (x ^ 3 + 3) / 7
  }
g(1)

## [1] 0.5714286

Function of Fixed Point Iteration

Fixed_PIT()
“rlist” library was used

Fixed_PIT <- function(x, es) {
  i = 0
  ea = 1.1 * es
  x0 = x
  newlist<- list()
  while (ea > es) {
    xi <- g(x0)
    ea <- abs(xi - x0) / xi
    
    looplist <- list(i,x0, xi, ea)
    newlist  <- list.append(newlist, looplist)
      
    i=i+1
    x0=xi
  }
  df <-  as.data.frame(do.call(rbind, newlist))
  list_name <- list("iteration",
                    "x(i)",
                    "x(i+1)",
                    "Error")
  names(df) <- c(list_name)
  print(df)

  cat("\n", "x= ",x0,
      "\n","alpha= ",round(x0,3))
  
}

Check the function

Fixed_PIT(2,0.00001)

##   iteration      x(i)    x(i+1)        Error
## 1         0         2  1.571429    0.2727273
## 2         1  1.571429 0.9829238    0.5987288
## 3         2 0.9829238 0.5642345    0.7420485
## 4         3 0.5642345 0.4542329    0.2421701
## 5         4 0.4542329 0.4419601   0.02776891
## 6         5 0.4419601 0.4409039  0.002395473
## 7         6 0.4409039 0.4408157 0.0002000918
## 8         7 0.4408157 0.4408084 1.666713e-05
## 9         8 0.4408084 0.4408078 1.388007e-06
## 
##  x=  0.4408078 
##  alpha=  0.441

REFRENCE
How to show the images in Rmarkdown: https://stackoverflow.com/questions/38333691/r-markdown-putting-an-image-in-the-top-right-hand-corner-of-html-and-moving-tit