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# HW5 - COT4501 Spring 2012 Homework V This assignment has...

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COT4501 Spring 2012 Homework V This assignment has seven problems. The assignment is due in class on Thursday, March 29, 2012. There are seven regular problems and two computer problems (using MATLAB). For written problems, you need to show your work and it is insufficient to just give the results or answers. For the computer problems, turn in your results (e.g., graphs, plots, simple analy- sis and so on) and also a printout of your (MATLAB) code. Problem 1 (15pts) 1. Suppose you are using an iterative method to solve a nonlinear equation f ( x ) = 0 for a root that is ill-conditioned, and you need to choose a convergence test. Would it be better to terminate the iteration when you find an iterate x k for which | f ( x k ) | is mall, or when | x k - x k - 1 | is small? Why? 2. If the errors at successive iterations of an iterative method are as follows, how would you characterize the convergence rate? (a) 10 - 2 , 10 - 4 , 10 - 8 , 10 - 16 , ... , (b) 10 - 2 , 10 - 4 , 10 - 6 , 10 - 8 , ... , 3. Suppose you are using the bisection method to find a zero of a nonlinear function, start- ing with an initial bracketing interval [ a, b ] . Give a general expression for the number of iterations that will be required to achieve an error tolerance of tol for the length of the final bracketing interval.

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HW5 - COT4501 Spring 2012 Homework V This assignment has...

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