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33 lines
1.0 KiB
Matlab
33 lines
1.0 KiB
Matlab
function [xList, errorList] = NewNewton (f, startingValue, errorAllowed)
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%
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%NewNewton (f, startingValue, errorAllowed)
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%This function computes the root of a function using the modified Newton's method
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%
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%Make sure the number of arguments is correct
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if(nargin ~= 3)
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error('That is an incorrect number of arguments')
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end
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%A few necesary things before we get started
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pkg load symbolic;
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warning('off','OctSymPy:sym:rationalapprox');
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%Constant variables
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maxIt = 50;
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fp = diff(f);
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fpp = diff(fp);
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%Variables
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oldAnswer = startingValue;
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newAnswer = 0;
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currentError = errorAllowed + 1;
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cnt = 1;
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%Loop until you find an answer within error or you reach the maximum number of itterations
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while((currentError >= errorAllowed) && (cnt < maxIt))
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newAnswer = oldAnswer - ((double(subs(f,oldAnswer)) * double(subs(fp,oldAnswer)))/(double(subs(fp,oldAnswer))^2 - (double(subs(f,oldAnswer)) * double(subs(fpp,oldAnswer)))));
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currentError = abs(newAnswer - oldAnswer);
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xList(end+1) = newAnswer;
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errorList(end+1) = currentError;
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oldAnswer = newAnswer;
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end
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end
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