 # Matlab Programming Problems

## Solution Preview

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function [x,Emaxs] = crude (f, xL, xU, Edes, display)
% CUDE Finds a minimum by performing a bisection like search
% Inputs: f = a function of one variable
%         xL = lower bound of region containing minimum
%         xU = upper bound of region containing minimum
%         Edes = function stops when x is guaranteed within Edes of minimum
%         display = display option (0 = no display (default), 1 = display)
% Outputs: x - estimate of minimum
%          Emaxs - value of Emax as a function of iteration number k;
if nargin < 5; display = 0; end

if display
fprintf ...
('    N       xL          xA          xB          xU          Emax\n');
end

functionCount = 0;

for k = 0 : 1000

Emax = (xU - xL) / 2;
Emaxs(k+1)=Emax;

xA = xL + 0.49 * (xU - xL); fxA = f(xA);
xB = xL + 0.51 * (xU - xL); fxB = f(xB);
functionCount = functionCount + 2;

if display
fprintf ('%5d %12.6f %12.6f %12.6f %12.6f %12.6f\n', ...
k, xL, xA, xB, xU, Emax);
end

if Emax <= Edes
x = (xL + xU) / 2; % take midpoint as final answer
if display
% the last two function evaluations weren't actually needed
% (the results weren't used) and could be eliminated
fprintf ('Tolerance achieved after %d function evaluations.\n', ...
functionCount - 2);
end...
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