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PRECONDITIONING A CLASS OF FOURTH ORDER PROBLEMS BY OPERATOR SPLITTING
parabolic problems fourth order problems preconditioning
2015/12/11
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...
PRECONDITIONING TECHNIQUES IN FRAME THEORY AND PROBABILISTIC FRAMES
Parseval frame Scalable frame Fritz John Theorem Probabilistic frames frame potential continuous frames
2015/12/10
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...
“PRECONDITIONING” FOR FEATURE SELECTION AND REGRESSION IN HIGH-DIMENSIONAL PROBLEMS
Model selection prediction error lasso
2015/8/21
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 ...
Stability and preconditioning for a hybrid approximation on the sphere
radial basis functions approximation on the sphere
2010/12/9
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...
PRECONDITIONING HIGHER ORDER FINITE ELEMENTSYSTEMS BY ALGEBRAICMULTIGRID METHOD OF LINEAR ELEMENTS
2007/12/12
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...