Lorenzo Isella wrote:
>
> Hello,
> And sorry for the late reply.
> You see, my problem is that it is not known a priori whether I have one
> or two zeros of my function in the interval where I am considering it;
> on top of that, does BBsolve allow me to select an interval of variation
> of x?
> Many thanks
>
> Lorenzo
>
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)
}
----
--
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