Numerical Analysis I Math 5070

HW Guidelines

All submitted solutions must be legible, organized, and always convey your understanding. Include reasoning whether the problem explicitly calls for it or not.

You are encouraged to discuss homework problems with each other and to learn from each other. However, the work submitted must be written up individually. Help received from others must be acknowledged by a note at the beginning of your assignment.

Academic integrity policies will be strictly enforced. Please be advised that you are responsible for making yourself aware of and understanding the policies and procedures in the Undergraduate and Graduate Catalogs that pertain to Academic Honesty. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. [The policies can be found at under Academic Policies, Student Rights and Responsibilities.] If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s). If you believe you are not responsible, you will have the opportunity for a hearing. You should consult with me if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.

Problems will cover both numerical and theoretical aspects of the course.

Numerical experimentation is an integral part of the course. Its goal is to reinforce and reflect theory, compare and contrast theory with practise, and make numerical and theoretical conjectures.

Here are some tips on what makes a good solution to a problem involving numerical computation. Not all of these may be applicable in very problem:

  1. In most cases, your Matlab code should be an m-file.
  2. Keep your code readable by using smart indentation (the Matlab editor can do this automatically), and including documentation and comments. Chapter 7 in the Matlab Guide by Higham and Higham contains excellent advice on how to do this.
  3. Do NOT submit reams of numerical output. This will almost certainly earn you negative credit. When appropriate, plot your numerical data. Use the subplot command to get multiple plots on the same page.
  4. Describe the design of your experiment. If you are comparing Method A with Method B, consider comparing the performance (for example, in terms of efficiency and accuracy) of each of the methods against a standard benchmark. A benchmark could be the exact solution computed by analytical (rather than numerical) means, or it could be a different method (which could be a built-in Matlab function).
  5. Describe the test data, and why you chose it. Do the same for any other design parameters.
  6. Organize your output in a compact and readable fashion. Use format compact to suppress unnecessary line feeds. Calculate relative errors if appropriate; summarize results in a table.
  7. Annotate your output; by hand is ok, and even preferable at times!
  8. What do you observe? What does the output suggest? Can you explain your observations?
  9. What conclusions can you draw from your experiments? Why? How does theory compare with practise? For example, how do the mathematically exact solutions compare with the numerical ones? Or, can you prove by analytical means the patterns you've observed or been led to conjecture by numerical means?
  10. Does your experiment suggest directions for further exploration? New conjectures? Generalizations? Include any progress made on such investigations. You are encouraged to extend exercises in this manner, and carry out your own on-going investigations during the semester.

Some Matlab Tips 

  1. To save output to a file, you can use Matlab's diary command. To learn more, type help diary at the Matlab prompt.
  2. Creating special matrices:
    >> help ones
    >> help zeros
    >> help eye
    >> help diag
    Example (try this at home!): >> n = 5; a = 5*eye(n) - 2*diag(ones(n-1,1),1) + 3*diag(ones(n-1,1),-1);
  3. Formats: >> help format
    Useful formats are: format short, format long, format rat.
    Always use format compact when printing to save paper. Don't confuse format compact with format short .
  4. Entering a polynomial: >> help poly
    Finding its roots: >> help roots
    Finding its derivative: >> help polyder
    Evaluating a polynomial: >> help polyval
    Multiplying polynomials: >> help conv
    Dividing polynomials: >> help deconv
  5. Generating evenly spaced points for function evaluation: >> help linspace
  6. Plotting: >> help plot
    Multiple plots in the same window: >>help subplot

Niloufer Mackey
Last modified: Thu Aug 31 19:25:30 EDT 2017

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