Numerical issues in Linear Algebra
Big field,
b/c of practical importance,
and the theory seems interesting enough
(i.e., numerical linear algebra is rich enough to be interesting to study,
and a good intro generally)
some issues:
- robustness ?
- ill-conditioned
Brief notes:
Computing det
For computing det of a numerical matrix,
Gaussian elimination is most practical.
However, for computing characteristic polynomials,
expansion by minors works better.
[Gaussian elimination over a ring doesn't work so well]
Yeah, pity.
For finding eigenvectors,
Rayleigh quotient works better
than zeros of char poly (which is unstable)