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We develop preconditioners for systems arising from finite element discretizations of parabolic problems which are fourth order in space. We consider boundary conditions which yield a natural ...
Frames which are tight might be considered optimally conditioned in the sense of their numerical stability.This leads to the question of perfect preconditioning of frames,i.e., modification of a given...
In this chapter we survey two topics that have recently been investigated in frame theory. First, we give an overview of the class of scalable frames.These are (finite) frames with the property that e...
The recently introduced and characterized scalable frames can be considered as those frames which allow for perfect preconditioning in the sense that the frame vectors can be rescaled to yield a tight...
We consider regression problems where the number of predictors greatly exceeds the number of observations. We propose a method for variable selection that first estimates the regression function, yiel...
First order optimization methods often perform poorly on ill-conditioned optimization problems. However, by preconditioning the problem data and solving the preconditioned problem, the performance of ...
This paper proposes a new preconditioning scheme for a linear system with a saddle-point structure arising from a hybrid approximation scheme on the sphere, an approximation scheme that combines (loca...
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffnes...
This paper discusses the optimal preconditioning in the domain decomposition method for Wilson element. The process of the preconditioning is composed of the resolution of a small scale global prob...
A preconditioning method for the finite element stiffness matrix is given in this paper. The triangulation is refined in a subregion; the preconditioning process is composed of resolution of two regul...

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