Street-Fighting Mathematics by Sanjoy Mahajan

Author:Sanjoy Mahajan
Language: eng
Format: epub
Publisher: The MIT Press

where A and B are constants for you to determine. Use the method of easy cases (Chapter 2) to determine their values. (See [3] to check your values and for a proof of the completed formula.)

Problem 4.16 Quadratic convergence

Start with a0 = 1 and g0 = 1/ (or any other positive pair) and follow several iterations of the AM–GM sequence

Then generate and to check that (quadratic convergence).

Problem 4.17 Rapidity of convergence

Pick a positive x0; then generate a sequence by the iteration

To what and how rapidly does the sequence converge? What if x0 < 0?

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