newtons method matlab in javascript

To implement Newton's method in Javascript, you can follow these steps:

1. Define the function that you want to find the root of. For example, let's say you want to find the square root of a number x. Then, your function would be:

index.tsx
function f(x) {
  return x*x - a;
}
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2. Define the derivative of your function. In this case, the derivative of f(x) is 2*x.

index.tsx
function df(x) {
  return 2*x;
}
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3. Implement Newton's method using a while loop. You can set a maximum number of iterations to prevent an infinite loop. Also, set an initial guess x0.

index.tsx
function newtonMethod(a, eps) {
  let x0 = a/2;
  let x1 = 0;
  let n = 0;
  
  while (Math.abs(x1 - x0) > eps && n < 100) {
    x0 = x1;
    x1 = x0 - f(x0)/df(x0);
    n++;
  }
  
  return x1;
}
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4. Call the newtonMethod function with the value you want to find the root of and the desired level of accuracy. For example:

index.tsx
let a = 10;
let eps = 0.0001;
let sqrtA = newtonMethod(a, eps);
console.log(sqrtA);
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This will print the square root of a with a level of accuracy of eps to the console.

Note: This implementation assumes that the function is continuous and differentiable in the interval [a, b] and that the initial guess x0 is close enough to the root.