MATLAB: Find the least positive root of the equation y=cos(sqrt​(abs(polyv​al(p,x))))​-sin(x)/2 with the use of fzero

fzero

what function should i create and what i should do after

Best Answer

Similarly to your earlier Question:
p = polyfit(x,y,7);                                     % Fit Polynomial
P = @(x,p) polyval(p,x);
f = @(x,p) cos(sqrt(abs(P(x,p)))) - sin(x)/2;           % Function
f_root = fzero(@(x) f(x,p), 1);                         % Find Single Root
xv0 = linspace(0, 5, 100);                              % Vector Of Initial Estimates For Multiple Roots
for k1 = 1:length(xv0)                                  % Find Multiple Roots
    f_root_v(k1) = fzero(@(x) f(x,p), xv0(k1));         % Find Vector Of Roots
end
roundn = @(x,n) round(x .* 10.^n)./10.^n;               % Round ‘x’ To ‘n’ Digits, Emulates Latest ‘round’ Function
function_roots = unique(roundn(f_root_v, 4));           % Find Unique Roots
EDIT — To find the least positive root, add this line:
LeastPositiveRoot = min(function_roots(function_roots > 0))
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