Question

Apply the false position method to find the root for the following equation f(x)=x3

-x-1=0 in the
range 1

Answer 1

Answer:

False Position method (regula falsi method) Algorithm & Example-1 f(x)=x^3-x-1.

Bisection method converges slowly. Here while defining the new interval $ [a_{n}, b_{n}]$ the only utilization of the function $ 'f(x)'$ is in checking whether $ f(a_{n})f(b_{n})<0$ but not in actually calculating the end point of the interval. False Position or Regular Falsi method uses not only in deciding the new interval $ [a_{n}, b_{n}]$ as in bisection method but also in calculating one of the end points of the new interval. Here one of end points of $ [a_{n}, b_{n}]$ say $ w$ is calculated as a weighted average defined on previous interval as