Tag: numerical methods


Computing Square Roots: Part 2: Using Continued Fractions

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Continued Fractions

Let's start part 2 of our discussion of computing square roots by talking about continued fractions. When we first learn mathematics, we learn to count in the base 10 system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. We can construct representations of all of the integers using these 10 digits, by arranging them in a different order. So, for example, saying 125 is equivalent to saying …




Computing Square Roots: Part 1: Using Newton's Method

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Newton's Method for Finding Roots of Equations

Suppose we have a function \(f(x)\) and we want to compute values of \(x\) for which \(f(x)=0\). These values of \(x\) are called the roots of \(f(x)\).

We can compute the roots using Newton's Method, which utilizes the derivative of the function to iteratively compute the roots of the function.

Newton's method begins with an initial guess. It evaluates the derivative …