Newton's Method for calculating the square root

MySqrt <- function(x, eps = 1e-06, itmax = 100, verbose = FALSE) {
    newtroot <- c()
    for (j in 1:length(x)) {
        j <- j
        Sqrt <- x[j]/2
        for (i in 1:itmax) {
            if (x[j] < 0 && verbose == TRUE) {
                print("Warning: input must be greater than 0!")
            }
            if (x[j] < 0) {
                Sqrt <- NaN
                newtroot[j] <- NaN
                break
            }
            if (verbose == TRUE) {
                Iteration <- i
                print(sprintf("Iteration %d: %f", Iteration, Sqrt))
            }
            if (x[j] == 0) {
                Sqrt <- 0
                newtroot[j] <- Sqrt
            }
            if (abs(Sqrt * Sqrt - x[j]) < eps) {
                newtroot[j] <- Sqrt
                break
            } else {
                Sqrt <- (Sqrt + x[j]/Sqrt)/2
                newtroot[j] <- Sqrt
            }
        }
        if (verbose == TRUE && length(x) > 1) {
            print(Sqrt)
        }
    }
    return(newtroot)
}

12 * MySqrt(0:2)

## [1]  0.00 12.00 16.97

MySqrt(1/7)

## [1] 0.378

MySqrt(-2:4, verbose = T)

## [1] "Warning: input must be greater than 0!"
## [1] NaN
## [1] "Warning: input must be greater than 0!"
## [1] NaN
## [1] "Iteration 1: 0.000000"
## [1] 0
## [1] "Iteration 1: 0.500000"
## [1] "Iteration 2: 1.250000"
## [1] "Iteration 3: 1.025000"
## [1] "Iteration 4: 1.000305"
## [1] "Iteration 5: 1.000000"
## [1] 1
## [1] "Iteration 1: 1.000000"
## [1] "Iteration 2: 1.500000"
## [1] "Iteration 3: 1.416667"
## [1] "Iteration 4: 1.414216"
## [1] "Iteration 5: 1.414214"
## [1] 1.414
## [1] "Iteration 1: 1.500000"
## [1] "Iteration 2: 1.750000"
## [1] "Iteration 3: 1.732143"
## [1] "Iteration 4: 1.732051"
## [1] 1.732
## [1] "Iteration 1: 2.000000"
## [1] 2

## [1]   NaN   NaN 0.000 1.000 1.414 1.732 2.000

MySqrt(-2:4)

## [1]   NaN   NaN 0.000 1.000 1.414 1.732 2.000

sqrt(-2:4)

## Warning: NaNs produced

## [1]   NaN   NaN 0.000 1.000 1.414 1.732 2.000

MySqrt(2:4)

## [1] 1.414 1.732 2.000

sqrt(2:4)

## [1] 1.414 1.732 2.000