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Kyle Drerup

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Vanteon Corporation
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DSP for Communications, image processing, radionavigation

 

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14 Nov 2010 Screenshot Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup newtons method, root finding, numerical analysis, ndimensional, optimization 7 9
  • 4.5
4.5 | 2 ratings
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22 Oct 2012 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup

@ Andrew Knyazev,

If there are >n equations, and only n variables, this method can solve for the "least-squares solution".
22 Oct 2012 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup

@Xu,

Convergence isn't guaranteed. If your initial estimate isn't in the "Region of Convergence", then it will not converge.

It depends on your initial estimate.

14 Apr 2011 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup

There is an error with your input.
Read the example carefully.

13 Apr 2011 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup

@ abdallah:

(d(b^2 -10)/db evaluated @ b = 0 ) is 0.

The example given in the m-file has two solutions. a = 15, b = sqrt(10) and a = 15, b = -sqrt(10).

For the method to converge, your starting point must be sufficiently near a solution, and should have a derivative with respect to all variables somewhere along the path of convergence.

Your starting point of [0,0] gives 15,0 on the first iteration. This stays on this point for all successive iterations, because d(F1)/da = 0 and d(F2)/db = 0 at [a,b] = [15,0].

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22 Oct 2012 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup Drerup, Kyle

@ Andrew Knyazev,

If there are >n equations, and only n variables, this method can solve for the "least-squares solution".
22 Oct 2012 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup Drerup, Kyle

@Xu,

Convergence isn't guaranteed. If your initial estimate isn't in the "Region of Convergence", then it will not converge.

It depends on your initial estimate.

22 Oct 2012 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup Xu

Work for relatively large n? I tried n=9, but Matlab is down.

Here are my codes:

delta=[-1 1 -1 1 -1];
F=[delta(1)*(cos(x5)+cos(2*x5+x1)+cos(3*x5+x2)+cos(4*x5+x3)+cos(5*x5+x4)) - delta(2)*(cos(x6)+cos(2*x6+x1)+cos(3*x6+x2)+cos(4*x6+x3)+cos(5*x6+x4));
delta(2)*(cos(x6)+cos(2*x6+x1)+cos(3*x6+x2)+cos(4*x6+x3)+cos(5*x6+x4)) - delta(3)*(cos(x7)+cos(2*x7+x1)+cos(3*x7+x2)+cos(4*x7+x3)+cos(5*x7+x4));
delta(3)*(cos(x7)+cos(2*x7+x1)+cos(3*x7+x2)+cos(4*x7+x3)+cos(5*x7+x4)) - delta(4)*(cos(x8)+cos(2*x8+x1)+cos(3*x8+x2)+cos(4*x8+x3)+cos(5*x8+x4));
delta(4)*(cos(x8)+cos(2*x8+x1)+cos(3*x8+x2)+cos(4*x8+x3)+cos(5*x8+x4)) - delta(5)*(cos(x9)+cos(2*x9+x1)+cos(3*x9+x2)+cos(4*x9+x3)+cos(5*x9+x4));
-sin(x5)-2*sin(2*x5+x1)-3*sin(3*x5+x2)-4*sin(4*x5+x3)-5*sin(5*x5+x4);
-sin(x6)-2*sin(2*x6+x1)-3*sin(3*x6+x2)-4*sin(4*x6+x3)-5*sin(5*x6+x4);
-sin(x7)-2*sin(2*x7+x1)-3*sin(3*x7+x2)-4*sin(4*x7+x3)-5*sin(5*x7+x4);
-sin(x8)-2*sin(2*x8+x1)-3*sin(3*x8+x2)-4*sin(4*x8+x3)-5*sin(5*x8+x4);
-sin(x9)-2*sin(2*x9+x1)-3*sin(3*x9+x2)-4*sin(4*x9+x3)-5*sin(5*x9+x4);
];
tolerance = .01;
initial_est = ones(1,9);
solution = newton_n_dim(tolerance,initial_est,[x1,x2,x3,x4,x5,x6,x7,x8,x9],F);

All functions are sin/cos.... Cannot get a solution.

12 Oct 2011 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup Knyazev, Andrew

Simple, general and nice! The best I have on the block so far.

Missing: limit number of steps, check for stagnation. default for the tolerance.

Cannot you just always use F_prime_X\F_X ?

14 Apr 2011 Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup Drerup, Kyle

There is an error with your input.
Read the example carefully.

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14 Nov 2010 Screenshot Newton Method in N dimensions Simple implementation of Newton's method, in n dimensions, taking input of >=n equations. Author: Kyle Drerup newtons method, root finding, numerical analysis, ndimensional, optimization 7 9
  • 4.5
4.5 | 2 ratings

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