Question

Which of the following is a method to solve simple non-linear equations by numerical method

• A. Lagrange Method
• B. Bolzano Weistras Method
• C. Newton Raphson Method
• D. Minimum distance method

Hint:

The Newton-Raphson method features a quadratic rate of convergence (order 2), which is faster than the linear convergence of the Bisection method.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A non-linear equation $f(x) = 0$ is solved numerically by generating a sequence of successive approximations that converge to the true root.

Step 2: Detailed Explanation:
Let us evaluate the options:
- Lagrange Method: Used primarily for polynomial interpolation or optimization with constraints.
- Bolzano-Weierstrass Theorem: A fundamental theorem in real analysis regarding bounded sequences; it is not an algorithmic solving method.
- Newton-Raphson Method: An iterative numerical method that uses the first derivative of the function to rapidly find successive, better approximations to the roots of a non-linear equation:
\[ x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)} \]
- Minimum distance method: Primarily used in classification, pattern recognition, or statistics.
Therefore, the Newton-Raphson Method is the correct numerical solver for non-linear equations.

Step 3: Final Answer
The correct option is (C).