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Author: Numerically-Stable

Intro2Matlab/arrays_demo.mlx

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+function [a, b] = bracket_root_bisection1(f, a, b)
+% single step bisection search for bracekting a root
+% takes a bracket containing a root as input 
+% gives a reduced(half) bracket containing root as output
+
+
+fa = f(a);
+fb = f(b);
+
+% Checking for sign, if same sign, no root exists
+if fa*fb > 0
+    error('Root not bracketed in the interval');
+end
+
+% else continuing
+c = (a+b)/2;
+fc = f(c);
+
+if fc == 0
+    % Found the root exactly
+    a = c;
+    b = c;
+    return;
+elseif fa*fc < 0
+    % Root is in the interval [a,c]
+    b = c;
+    fb = fc;
+else
+    % Root is in the interval [c,b]
+    a = c;
+    fa = fc;
+end
+
+
+
+
+end

Intro2Matlab/bracket_root_bisection1.m

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+% inputs
+a = -3 ;       % Left bracket
+b = 1 ;        % Right bracket
+tol = 1e-3 ;   % Tolerance
+f = @(x) x^3 ; % function
+
+iter = 0;
+while abs(a-b)/2 > tol
+    iter = iter + 1;
+    [a, b] = bracket_root_bisection1(f, a, b);
+    
+
+    if abs(a-b)/2 <= tol
+        root = (a+b)/2;
+    end
+end

Intro2Matlab/final.mlx

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+% inputs
+a = -3 ;       % Left bracket
+b = 1 ;        % Right bracket
+f = @(x) x^3 ; % function
+
+
+
+fa = f(a);
+fb = f(b);
+
+% Checking for sign, if same sign, no root exists
+if fa*fb > 0
+    error('Root not bracketed in the interval');
+end
+
+% else continuing
+c = (a+b)/2;
+fc = f(c);
+
+if fc == 0
+    % Found the root exactly
+    a = c;
+    b = c;
+    return;
+elseif fa*fc < 0
+    % Root is in the interval [a,c]
+    b = c;
+    fb = fc;
+else
+    % Root is in the interval [c,b]
+    a = c;
+    fa = fc;
+end
+
+
+