AppliedNumeric answer

Iterating $x_{k+1} = \cos x_k$ converges to the fixed point $x^* \approx 0.739$ . By roughly what factor does the error shrink each step, to three decimals?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

The worked solution is in Premium

The answer, the full working and the one idea to take away – for this and all 1,322 questions in the bank. Answer it in practice and your working is marked, with a known mistake named when you make one.

Start the 7-day free trial Practise it with Premium

Learn the method

Root finding, with implied volatility as the worked case

Reported in interviews at

Citadel, Two Sigma

Iterating xk+1=cos⁡xkx_{k+1} = \cos x_kxk+1​=cosxk​ converges to the fixed point x∗≈0.739x^* \approx 0.739x∗≈0.739. By roughly what factor does the error shrink each step, to three decimals?

More numerical methods questions

Iterating $x_{k+1} = \cos x_k$ converges to the fixed point $x^* \approx 0.739$ . By roughly what factor does the error shrink each step, to three decimals?