1 Homework CS1515 Due: January 21, 2005 by 11:59pm Submit a zip-file containing your solutions and a text-file listing the names of your mfiles and their corresponding problem number (for example: problem A (1) bellcurve.m problem A (2) rect2polar.m ... to the digital dropbox in Blackboard. A) Create an m-file to solve the following problems from Chapra's text: 1) Problem 2.2, page 29 2) Problem 3.6, page 56 3) Problem 3.9, page 57
_
B) Write a function to evaluate the polynomial shown below using Horner's method p(x) = a1xn-1 + a2xn-2 +... + an-1x + an at x = c. Your parameters are a vector v = [a1 a2 a3 . . . an-1 an] and a real number c. For example, the following execution evaluates 5x3 - 3x2 + 7x + 2 at x = 4.
QuestionB([5 -3 7 2],4) ans = 302
C) Write a function with one parameter n that equals the size of a random vector [use rand(m,1) to generate a random vector of length m]. 1) Compute the sum of the elements in this vector in generated order (1st to last), 2) Compute the sum of the elements in this vector in reverse order (last to 1st), 3) Compute the sum of the elements in this vector sorted in increasing order, 4) Compute the sum of the elements in this vector sorted in decreasing order. Explain why the answers are all different.
sumRandomVector(120000) sumGenOrder = 5.992251152396442e+004 sumIncOrder = 5.992251152396477e+004 sumDecOrder = 5.992251152396395e+004 = sumRevOrder 5.992251152396531e+004
5 __ _
D) Derive an iterative algorithm to determine the fifth root of x from the equation y = x, where x is any real number. You may only use multiplication and square roots to build your iteration rule x = g(x). Implement your algorithm as a Matlab function with two parameters x and d to compute the fifth root of x to d decimal places of accuracy. Recall, d is defined as Absolute error = |yk trueroot| = 10-d Note: you are allowed to compute the trueroot in your function to accomplish the above test. Also, choose |x| as the initial guess.
format long g questionD(2.861381721051424e+015,1) ans = 1234.03821013704 questionD(2.861381721051424e+015,2) ans = 1234.00537322903 questionD(2.861381721051424e+015,4) ans = 1234.00003984655
E) Modify the solution of ...