## What is ridders method?

Ridders’ method is a root-finding method based on the regula falsi method that uses an exponential function to fit a given function bracketed between x0 and x1 . to transform the function into a straight line.

**Which is the faster convergence method in finding root?**

Ridders’ method is a hybrid method that uses the value of function at the midpoint of the interval to perform an exponential interpolation to the root. This gives a fast convergence with a guaranteed convergence of at most twice the number of iterations as the bisection method.

### Which of the following is the fastest method to find the root of equation?

The fastest root-finding method we have included is Newton’s method, which uses the derivative at a point on the curve to calculate the next point on the way to the root. Accuracy with this method increases as the square of the number of iterations.

**What is the formula of Regula Falsi method?**

= 0 then c is the root. Selecting c by the above expression is called Regula-Falsi method or False position method….REGULA-FALSI METHOD.

c = b – | f(b) * (b-a) |
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f(b) – f(a) |

#### Which method converges fastest?

Newton’s Method is a very good method When the condition is satisfied, Newton’s method converges, and it also converges faster than almost any other alternative iteration scheme based on other methods of coverting the original f(x) to a function with a fixed point.

**Which of the following method has highest rate of convergence?**

It is a well-known fact that, for solving algebraic equations, the bisection method has a linear rate of convergence, the secant method has a rate of convergence equal to 1.62 (approx.) and the Newton-Raphson method has a rate of convergence equal to 2.

## Which method has slow convergence?

Explanation: Rate of convergence of the Newton-Raphson method is generally Linear. It states that the value of root through the Newton Raphson method converges slowly.

**Does secant method converges faster than bisection method?**

Advantages of secant method: 1. It converges at faster than a linear rate, so that it is more rapidly convergent than the bisection method. 2. It does not require use of the derivative of the function, something that is not available in a number of applications.

### What is the order of convergence of false position method?

In false position method, the sequence of approximation is {x1, x2, xn}that converges at x. Let en: error is given as xn – x. The sequence converges if |en| → 0 as n → ∞.

**What is the order of convergence of Regula Falsi?**

Detailed Solution

Iterative Method | Convergence |
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Regula-Falsi method | Order – 1 |

Newton-Raphson method | Order – 2 |

Secant method | Order – 1.62 |

Successive approximation method | Order – 1 |