You are encouraged to discuss homework problems with each other
and to learn from each other. Help received from others must be
acknowledged by a note at the beginning of your assignment. Under no
circumstances is it acceptable for you to copy each other's work.
See the section on
Academic Integrity .
You are strongly advised to do your homework assignments promptly.
Problems will cover both numerical and theoretical
aspects of the course.
Solutions must be legible, organized and always include reasoning
(whether the problem explicitly calls for it or not).
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:
- Your Matlab code should either be a script or an m-file,
created using the built-in Matlab editor. See Chapter 2 of our text.
- Your code must follow the
standard recommendations regarding documentation, comments and indentation.
- 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).
Describe the test data,
and why you chose it.
Do the same for any other design parameters.
Do NOT submit reams of output.
This will almost certainly earn you negative credit.
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.
- When appropriate, plot your numerical data.
Learn about Matlab's subplot command which allows you to display
multiple plots in the same graphing window.
- All output, numerical and graphical, must be annotated, clearly identifying the features
of interest. Annotations by hand are okay, even preferable at times.
- Discussion of your output should be alongside your output.
Don't make the reader keep turning pages back and forth.
- What do you observe?
What does the output suggest?
Can you explain your observations?
What conclusions can you draw from your experiments?
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?
Does your experiment suggest directions for further exploration?
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.
- To save output to a file, you can use Matlab's diary command.
To learn more, type help diary at the Matlab prompt.
- Creating special matrices:
>> help ones
>> help zeros
>> help eye
>> help diag
>> n = 5; a = 5*eye(n) - 2*diag(ones(n-1,1),1) + 3*diag(ones(n-1,1),-1);
- Formats: >> help format
Useful formats are: format short, format long, format
Always use format compact when printing to save paper.
Don't confuse format compact with format short .
- 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
- Generating evenly spaced points for function evaluation:
>> help linspace
- Plotting: >> help plot
Multiple plots in the same window: >>help subplot
Wed Dec 28 22:31:13 EST 2016
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