hw2 - e n the error of the n-th approximation ( e n = p n x...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework 2 – Math 104A, Fall 2010 Due on Tuesday, October 12th, 2010 Section 2.1: 6, 12, 14, 16, and 20. Section 2.2: 1, 2, 3, 4, 11.a, 11.b, 11.c, and 23. Additional problem: Consider the iteration in Newton’s method: p n +1 = g ( p n ) where g ( x ) = x f ( x ) f ( x ) Prove that if f ( x ) = 0, and f ( x ) n = 0, then g ( x ) = 0. Deduce from this that the convergence of Newton’s method is quadratic, i.e., if we denote by
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: e n the error of the n-th approximation ( e n = p n x ), then e n +1 Ke 2 n for some K > 0, as long as the initial iterate p is suFciently close to x . You may assume that f has innitely many continuous derivatives. 1...
View Full Document

This note was uploaded on 12/26/2011 for the course MATH 104a taught by Professor Staff during the Fall '08 term at UCSB.

Ask a homework question - tutors are online