CS3414 Afterclass Notes --- 18 June, 2002
Linear Systems (Chapter 6)
- The problem Ax=b: find x, given
A and b.
- This is a very important problem, arising in many
scientific computing applications.
- Typical computational science codes need to solve very
large instances of this problem, and often many
different instances of this problem.
- An important theme in algorithms for Ax=b is
exploiting structure, e.g., sparsity, symmetry,
- Another important theme is algorithms that are
resource-aware, e.g., algorithms that use the memory
- Some facts from linear algebra.
We looked at several equivalent properties that imply that
there is a unique solution. Most important for our purposes is
the idea that A is nonsingular (invertible) and
that Gaussian Elimination works (with the huge assumption of