Creating a Table for Newton's Method

Question

Kevin Osborn 2021-10-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1465484-creating-a-table-for-newton-s-method

回答： Walter Roberson 2021-10-2

I am trying to creat a table for different values that Newton's method approximates for different starting values. I have the following for the method.

x0 = 0.0:0.1:8;
for j = 1:numel(x0)
    f = @(x) 2*exp(-2*x) + 4*sin(x) - 2*cos(2*x);
    fp = @(x) 4*(-exp(-2*x) + sin(2*x) + cos(x));
    x(1) = x0(j);
    N = 50; 
    tol = 1e-6;
    n = 2; 
    nfinal = N + 1; 
    while (n <= N + 1)
      fe = f(x(n - 1));
      fpe = fp(x(n - 1));
      x(n) = x(n - 1) - fe/fpe;
      if (abs(fe) <= tol)
        nfinal = n; 
        break;
      end
      n = n + 1;
    end
end

I think I need to add something in the for loop to save the values, but how do I make a table out of this? I would like one collumn to be all the x(0) values and another collumn to be all the values that each x(0) converges to.

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Answer 1

Walter Roberson 2021-10-2

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1465484-creating-a-table-for-newton-s-method#answer_800324

在 MATLAB Online 中打开

The NaN is because you have a 0 divided by 0

x0 = (0.0:0.1:8).';
results = table(x0);
results.x_final = nan(size(x0));
for j = 1:numel(x0)
    f = @(x) 2*exp(-2*x) + 4*sin(x) - 2*cos(2*x);
    fp = @(x) 4*(-exp(-2*x) + sin(2*x) + cos(x));
    x(1) = x0(j);
    N = 50; 
    tol = 1e-6;
    n = 2; 
    nfinal = N + 1; 
    while (n <= N + 1)
      fe = f(x(n - 1));
      fpe = fp(x(n - 1));
      x(n) = x(n - 1) - fe/fpe;
      if (abs(fe) <= tol)
        nfinal = n;
        break;
      end
      n = n + 1;
    end
    results.x_final(j) = x(nfinal);
end
results
results = 81×2 table
x0x_final______________

      0            NaN
    0.1     9.3521e-05
    0.2     8.9191e-05
    0.3     0.00012689
    0.4     0.00015928
    0.5     9.2778e-05
    0.6     0.00010227
    0.7     0.00010719
    0.8     0.00010587
    0.9     9.5182e-05
      1     0.00013702
    1.1     0.00017184
    1.2    -0.00011787
    1.3    -0.00011629
    1.4    -9.1689e-05
    1.5    -0.00016472