The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of refinement to enhance methods sparse based approximate factorizations. In doing so, we first develop a new error analysis LU- and GMRES-based under general mo...

We examine the behavior of Newton’s method in floating point arithmetic, allowing for extended precision in computation of the residual, inaccurate evaluation of the Jacobian and unstable solution of the linear systems. We bound the limiting accuracy and the smallest norm of the residual. The application that motivates this work is iterative refinement for the generalized eigenvalue problem. We...

We present an approach for motion primitive learning and refinement for a humanoid robot. The proposed teaching method starts with observational learning and applies iterative kinesthetic motion refinement. Observational learning is realized by a marker control approach. Kinesthetic teaching is supported by introducing the motion refinement tube in order to avoid to disturb other joints acciden...

Because of scaling problems, Gaussian elimination with pivoting is not always as accurate as one might reasonably expect. It is shown that even a single iteration of iterative refinement in single precision is enough to make Gaussian elimination stable in a very strong sense. Also, it is shown that without iterative refinement row pivoting is inferior to column pivoting in situations where the ...