The linear least squares problem is a computational problem of primary importance in many
applications. Assume for example that one wants to fit a linear mathematical model to given …

We are delighted that SIAM is republishing our original 1983 book after what many in the
optimization field have regarded as “premature termination” by the previous publisher. At 12 …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

This paper presents a numerically stable non-iterative algorithm for fitting an ellipse to a set
of data points. The approach is based on a least squares minimization and it guarantees an …

This paper introduces an extension of minimum variance beamforming that explicitly takes
into account variation or uncertainty in the array response. Sources of this uncertainty …

Reconstructing an arbitrary configuration of 3D points from their projection in an image is an
ill-posed problem. When the points hold semantic meaning, such as anatomical landmarks …

Discretization of linear inverse problems generally gives rise to very ill-conditioned linear
systems of algebraic equations. Typically, the linear systems obtained have to be …

In this paper we evaluate several methods of tting data to conic sections. Conic tting is a
commonly required task in machine vision, but many algorithms perform badly on …

This computationally oriented book describes and explains the mathematical relationships
among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and …

Many algorithms in recent computational statistics are variations on a common theme. In this
paper we discuss four such classes of algorithms. Or, more precisely, we discuss a single …