Damped Gauss Newton iteration (how to extend a given matrix)

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Christoffer Thornvall 2015-11-6

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https://ww2.mathworks.cn/matlabcentral/answers/253563-damped-gauss-newton-iteration-how-to-extend-a-given-matrix

评论： Image Analyst 2015-11-6

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Hi so I've ran in to a problem I was wondering if someone could help me resolve. This is my script:

tvec = [0 0.2 0.4 0.6 0.8]'; Pvec = [5.1 5.9 6.4 7.5 8.3]';

F =@(x) x(1)*(exp(x(2).*tvec)) - Pvec;

dFdP0 = @(x) exp(x(2).*tvec);

dFdr = @(x) x(1).*tvec*exp(x(2)).*exp(tvec);

J =@(x) [dFdP0(x), dFdr(x)]; % Jacobianen

x = [5.1 0.5274]'; %[P0. r]

tolerans = 1e-8; [xm,countm] = GaussNewton(F,J,x,tolerans)

And my function:

function [x,count] = GaussNewton1(F,J,x,tolerans)

hnorm = 1;

count = 0;

L = 10

L = L^0.5;

n = size(x)

m = zeros(n,1)

I = eye(n,n)

I = I*L

while (hnorm > tolerans && count<100)

    h = J(x)\F(x);
    hnorm = norm(h, inf);
    x=x-h;
    count = count+1;
end

What I wanna do is add write something that looks like (J(x);I)\(F(x);m) but I don't know how to do this in matlab code. Like I wanna extend my jacobian with the I and my F with a column vector of m zeros. Any ideas?

/// Christoffer

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Image Analyst 2015-11-6

See this http://www.mathworks.com/matlabcentral/answers/13205-tutorial-how-to-format-your-question-with-markup

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