show that false position method converges linearly.
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Answer Posted / Mukesh Gupta
To show linear convergence of the false position method, we first need to calculate the error at each iteration: e_k = |x_k - x_*|, where x* is the actual root. We can then write the error at the next iteration in terms of the current error: e_{k+1} <= c * e_k^2, where c is a constant that depends on the function being solved and the initial guesses.nThis shows that the method converges linearly because the error decreases proportionally to the square of the previous error.
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