Title: Stable Solution of Quasiseparable Systems

The basis of this talk is a parameterization of a quasiseparable
matrix in terms of a nested product involving Householder
transformations and very sparse matrices having only a few nonzeros
each.  This parameterization has appealing numerical properties in
that the representation of a matrix is not sensitive; small
perturbations of the parameters correspond to small perturbations of
the matrix.  This is a property that is not easy to guarantee with
other parameterizations of rank structured matrices.

In part because of this insensitivity it is possible to use the
parameterization as the basis of a provably backward stable fast
linear system solver.  The talk will describe algorithms for computing
the parameterization and solving linear systems.  In addition, without
getting into the details of a full error analysis, it will describe
the numerical properties of the algorithms and the key points in a
proof of backward stability.