This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Homework 3, Solution Sketches Math 371, Fall 2011 1. (Rootfinding and Optimization) (a) (b) Approximate this local maximum using six iterations of the bisection method with starting interval [4 , 6]. (see table) (c) Approximate this local maximum using six iterations of the two fixed point methods (Secant and Newton). For Newton’s Method, use p = 4. For the Secant Method, use p = 6 and p 1 = 4. (see table) (d) What is your best estimate for p , the location of the maximum? ≈ 4.917185925287 (e) Compare the three algorithms using the following two tables. Table 1: Approximation p n versus iteration number n n Bisection Secant Newton 5.0000000 4.000000000000 4.000000000000 1 4.5000000 6.000000000000 5.102942595731 2 4.7500000 5.064897139287 4.911129833126 3 4.8750000 4.850826860926 4.917182043699 4 4.9375000 4.918381747299 4.917185925286 5 4.9062500 4.917193617001 4.917185925287 6 4.9218750 4.917185924293 4.917185925287 Table 2: Absolute error  p n p  versus iteration number n n Bisection...
View
Full
Document
This note was uploaded on 12/16/2011 for the course MATH 371 taught by Professor Krasny during the Fall '08 term at University of Michigan.
 Fall '08
 KRASNY
 Math

Click to edit the document details