The eigenvalue or real symmetric matrix as term project?

Question

If I wish to use the eigenvalue or real symmetric matrix as term project for numerical analysis for senior undergraduate, which size of the matrix should I restrict the original matrix? In the sense that it will not be too hard nor too easy. Also should I restrict the original matrix to be sparse. The required implementation language will be C++.

Answer 1

What element of the computation of eigenvalues do you wish to investigate?

The problems of large sparse matrices are quite different from those with multiple slightly different eigenvalues. (It is easy to find the smallest eigenvalue if it is isolated from the others and the matrix is small enough.)

Keeping the matrices small enough to stay in memory makes things easier, but also rules out many interesting problems.

Other factors include whether you only want to compute the eigenvalues or also the associated eigenvectors

Other possible projects include:

1. Comparing the performance of various algorithms

2. Instead of writing a program per se, writing a library that others can use.

You might want to look at "Numerical Recipes: The Art of Scientific Computing"

I haven't seen the new edition, but the old edition had a nice section on algorithms, but the code was very non-C++-ish. Rewriting any of the algorithms in good C++ library style would be a good project.