Fall2011-HW3-soln - Homework 3 Solution Sketches Math 371...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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.

Page1 / 2

Fall2011-HW3-soln - Homework 3 Solution Sketches Math 371...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online