[R] Finding Zeros of a Function

[Hans W Borchers]

Hans W Borchers wrote:
> 
> Let's see how many zeroes are there of the function sin(1/x) in the
> interval
> [0.1, 1.0].  Can you find out by plotting?
> 
> In the 1-dimensional case the simplest approach is to split into
> subintervals
> small enough to contain at most one zero and search each of these, e.g.,
> with 
> the secant rule --- or uniroot() if you like.
> 
> The following function will find 31 zeroes for sin(1/x) using subintervals
> of length 1/000, i.e. x <- seq(0.1, 1.0, len=1001); y <- sin(1/x); and
> call
> piecewise(x, y).
> 
> Hans Werner
> 
> ----
> piecewise <- function(x, y) {
> 	n <- length(x)
> 	zeros <- if (y[1] == 0) c(x[1]) else c()
> 	for (i in 2:n) {
> 		if (y[i]*y[i-1] >= 0) {
> 			if (y[i] == 0) zeros <- c(zeros, x[i])
> 		} else {
> 			x0 <- (x[i-1]*y[i] - x[i]*y[i-1])/(y[i] - y[i-1])
> 			zeros <- c(zeros, x0)
> 		}
> 	}
> 	return(zeros)
> }
> ----
> 

Sorry, I meant "how many zeroes are there in the interval [0.01, 1.0] ?" !
The following will find 31 zeroes, and these are all.

    x <- seq(0.01, 1.0, len=1001)
    y <- sin(1/x);
    piecewise(x, y)

Hans Werner

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