Tea Time Numerical Analysis · Problem 1.3.1

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · order-of-convergence

Problem

In Table 1.4, four sequences ⟨qn⟩\langle q_n \rangle, ⟨rn⟩\langle r_n \rangle, ⟨sn⟩\langle s_n \rangle, ⟨tn⟩\langle t_n \rangle all converge to e≈2.71828182845904e \approx 2.71828182845904. Using the formula α≈ln⁡∣pn+2−ppn+1−p∣ln⁡∣pn+1−ppn−p∣\alpha \approx \frac{\ln\left|\frac{p_{n+2}-p}{p_{n+1}-p}\right|}{\ln\left|\frac{p_{n+1}-p}{p_n-p}\right|} estimate the order of convergence α\alpha for each of the four sequences using several sets of three consecutive terms from Table 1.5.

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