afael Navarro nstituto de Ciencia de Materiales de Aragón ICMA onsejo Superior de Investigaciones Científicas-Universidad de Zaragoza, Facultad de Ciencias laza San Francisco s/n 0 009 Zaragoza, Spain -mail: [email protected] Abstract. A theoretical framework to formulate and solve the problem of obtaining the objective refraction of an eye from aberrometric data is presented. Matrix formalism...

For cases in which perfect model following is not possible for a particular desired model, a class of candidate models is defined that can be followed perfectly by the given plant. A candidate model that most closely matches the dynamics of the desired model is then determined through constrained parameter optimization. The result is perfect model following of a model that has an eigenstructure...

Symmetric positive semidefinite (SPSD) matrix approximation is an important problem with applications in kernel methods. However, existing SPSD matrix approximation methods such as the Nyström method only have weak error bounds. In this paper we conduct in-depth studies of an SPSD matrix approximation model and establish strong relative-error bounds. We call it the prototype model for it has mo...

An outstanding problem when computing a function of a matrix, f(A), by using a Krylov method is to accurately estimate errors when convergence is slow. Apart from the case of the exponential function which has been extensively studied in the past, there are no well-established solutions to the problem. Often the quantity of interest in applications is not the matrix f(A) itself, but rather, mat...

Symmetric positive semidefinite (SPSD) matrix approximation is an important problem with applications in kernel methods. However, existing SPSD matrix approximation methods such as the Nyström method only have weak error bounds. In this paper we conduct in-depth studies of an SPSD matrix approximation model and establish strong relative-error bounds. We call it the prototype model for it has mo...