How to solve (find zero) of nonanalitical function fzero or fsolve ?

I have a vector y(x) that does not necessarily have point on y = 0 axis (and is not analytical function).

How can I solve (find the zero crossing) without fitting.

For example:

y = [-1 -0.3 -4 -0.1 0.25 0.4 0.2 0.9  ]
x = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7]

I would like to solve for y(x)=0

Answer 1

[Star Strider]

This works:

y = [-1 -0.3 -4 -0.1 0.25 0.4 0.2 0.9];
x = [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7];

yx = find(y>0,1,'first');                   % Choose 1st ‘y’ Point >0
y0 = 0;
x0 = interp1(y(yx-1:yx),x(yx-1:yx),y0);     % Find Zero Cross Between Bracket Points

figure(1)
plot(x, y)
hold on
plot(x0, y0, 'bp')
hold off
grid

[Image Analyst]

Of course that's fitting a line between adjacent points, which makes perfect sense. Sam answer I would have given. I never did figure out why "not fitting" was a requirement. Who cares as long as it gets the job done? You could also use splines (demo attached).