Solve equation by fzeros

I'm solving the equation by using fzero.

My code is:

fzero(@(x) x-4*sin(x), -10)

Result just has ONE root. How to show ALL roots of equation by using fzero ?!

Answer 1

[Sam Chak]

@Hoang Vu Huy

The fzero requires initial guess. Pick the initial value that is closest to the root:

fzero(@(x) x - 4*sin(x), pi)

and it will return another solution.

Can also try this Taylor series expansion method to "guess" the initial values:

syms x
fun = x - 4*sin(x);
T9 = taylor(fun, x, 'Order', 9)
fplot([fun T9])
grid on
xlabel('x')
ylabel('f(x)')
legend('x - 4*sin(x)', 'Taylor9', 'location', 'northwest')

p = sym2poly(T9);
g = roots(p);
g(imag(g) ~= 0) = []    % initial guesses of the approximated roots

r1 = fzero(@(x) x - 4*sin(x), g(1))
r2 = fzero(@(x) x - 4*sin(x), g(2))
r3 = fzero(@(x) x - 4*sin(x), g(3))

T9 = x^7/1260 - x^5/30 + (2*x^3)/3 - 3*x

g =

0

-2.4661

2.4661

r1 = 0

r2 = -2.4746

r3 = 2.4746

Answer 2

[Star Strider]

It is straightforward to find all the roots.

One approach —

N = 6;
x = linspace(-N, N);
y = x-4*sin(x);

zxi = find(diff(sign(y)));                                  % Approximate Zero-Crossing Indices

for k = 1:numel(zxi)
    x0(k) = fzero(@(x) x-4*sin(x), x(zxi(k)));              % Calculate Exact Zero-Crossings
end

figure
plot(x, y)
hold on
plot(x0, zeros(size(x0)), 'rs')
hold off
grid
legend('$y(x) = x-4sin(x)$','$Roots$', 'Location','best', 'Interpreter','latex')

.