Some complexity considerations in sparse LU factorization

The talk will discuss unsymmetric sparse LU factorization based on

the Markowitz pivot selection criterium. The key question for the

author is the following: Is it possible to implement a sparse

factorization where the overhead is limited to a constant times

the actual numerical work? In other words, can the work be bounded

by o(sum(k, M(k)), where M(k) is the Markowitz count in pivot k.

The answer is probably NO, but how close can we get? We will give

several bad examples for traditional methods and suggest alternative

methods / data structure both for pivot selection and for the sparse

update operations.