MATH/CSCI-4800 Problem Set 6
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MATH/CSCI-4800
Due: Friday March 17, 2023
Problem Set 6
Submissions are due in the LMS by the end of the day. Also note that the use of syms in MATLAB is strictly forbidden.
1. (15 pts.) The following cubic polynomial has three real roots p(x) = 16x3 - 63x2 + 77x - 30
(a) Plot p(x) for .9 ≤ x ≤ 2.1 and indicate the locations of the three roots. What are the
exact roots of p(x)?
(b) Write a MATLAB code to run Newton’s method with x0 = 1.65 and discuss the conver-
gence.
(c) Write a MATLAB code to run the secant method starting with x0 = 1.65 and x1 = 1.5 and discuss the convergence?
(d) Write a MATLAB code to run the bisection method with the initial bracket [ .9, 2.1] and discuss the convergence.
2. (10 pts.) Plot the two curves in the uv -plane implied by the following systems. Then find all solutions exactly using simple algebra.
(a)
(b)
(c) {4(u)u(2)
3. (15 pts.) Write a MATLAB code to perform Newton’s method for the three systems from problem #2 above. Discus the choice of initial guess in relation to the root found by your code.
4. (10 pts.) Computer Problem 2.7 problem 4.
2023-03-18