How do I implement a while loop until convergence in R?

February 16, 2022

I want to code a while loop which iteratively fills values in a vector until its values converge. Here is a reproducible example :

vector <- c()
# initalize first and 2nd element
vector[1] <- 1
vector[2] <- 1 + exp(-2)

The ith element of the vector should be (1 + exp(-i)) and therefore this suite should converge, as n goes to infinity, difference between the (ith) and (i-th -1) element should goes to zero.
Let epsilon an arbitrarily small value :

epsilon <- 10E-3

The while loop I coded is :

# Fill the vector until difference between the i-th element and the element before it becomes negligible : 
while (vector[i]-vector[i-1] > epsilon){
  vector[i+1] <- vector[i] + exp(-i)
}

Which fails to create the requested vector.

>Solution :

It looks like you’re missing an initialization of the i object as well as a way to increment i:

vector <- c()
# initalize first and 2nd element
vector[1] <- 1
vector[2] <- 1 + exp(-2)

epsilon <- 10E-3

# initialize i
i <- 2

while (vector[i]-vector[i-1] > epsilon){
  
  vector[i+1] <- vector[i] + exp(-i)
  
  # increase i
  i <- i + 1
  
}

This example should terminate after i = 6