Trying to answer a math problem using newton's method but having problem in the function.

This is the last function when newton's method is applied:

I used z=log(x) in my function to make it easier to understand:

clc
x=0.25;
y=0;
while (y-x)<10^-4
    z=log10(x);
    y = x-((((x ^ 2)z-(x ^ 0.5)-20)2.x ^0.5)/(-1+4.x ^ (3/2)z+2.x ^ (3/2)))

Invalid expression. Check for missing multiplication operator, missing or unbalanced delimiters, or other syntax error. To construct matrices, use brackets instead of parentheses.

    x=y;
    
end

Answer 1

[Alan Stevens]

Matlab doesn't like implied multiplication

(x ^ 2)z  

should be

(x ^ 2)*z

etc.

Also, in Matlab

log(x)

is ln(x)

Answer 2

[Cris LaPierre]

You need to include the multiplication operator when coding your equation. Also, it is '*', not '.'. Nothing is inferred.

I think your conditional will be problematic, since the last line of your loop sets x equal to y.

x=0.25;
y=0;
while (y-x)<10^-4
    z=log10(x);
    y = x-((((x ^ 2)*z-(x ^ 0.5)-20)*2*x ^0.5)/(-1+4*x ^ (3/2)*z+2*x ^ (3/2)))
    x=y;
    
end

[Cris LaPierre]

+1 about log10 vs log for natural ln.

Also wanted to point out that you have created an infinite loop. Since x=y, (y-x) is 0, which is <1e-4. Since your condition will always be true, your loop will never end.

Just changing the < to > will prevent the infinite loop, but won't fix the issue that y=x. Consider creating a third variable to prevent this.

Also consider the case that the difference of (y-x) may be positive or negative. You may want your condition to compare to the absolute value of this difference.

Answer 3

[Voss]

Multiplication is * or .* but never . as in 4.x and never implicit as in (x^2)z

log10 is base-10 logarithm. log is natural logarithm.

z = log(x);
y = x-((((x^2)*z-(x^0.5)-20)*2*x^0.5)/(-1+4*x^(3/2)*z+2*x^(3/2)));