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Numerical Analysis

David Gleich

Purdue University

Spring 2016

Course number CS-51400, MATH-51400

Tuesday and Thursday, noon-1:15pm

Location Lawson B155

Homework 6

Please answer the following questions in complete sentences in a typed manuscript and submit the solution on blackboard by on April 11th at noon. (These will be back before the midterm.)

Problem 0: Homework checklist

Problem 1: Gautschi Exercise 4.1

The following sequences converge to as :

Indicate the type of convergence for each sequence in terms of

Problem 2: Implementing a core routine

  1. Using any method we've seen to solve a scalar nonlinear equation (bisection, false position, secant), develop a routine to compute using only addition, subtraction, multiplication, and division (and basic control structures) to numerical precision. (Use double-precision.)

  2. Compare the results of your method to the Matlab/Julia/Python function sqrt. Comment on any differences that surprise you.

Problem 3: Comparing the algorithms (Gautschi Machine Exercise 4.2)

Consider the problem . The only positive real root is located in . Compare the performance of bisection, false position, and the secant method in terms of the number of function evaluations to compute the solution to and full machine precision. For all these methods, use the boundary points (or use those as the first two points for secant).