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Given an $n \times n$ symmetric possibly indefinite matrix $A$, a modified Cholesky algorithm computes a factorization of the positive definite matrix $A+E$, where $E$ is a correction matrix. Since the factorization ...

Numerical solution of ill-posed problems is often accomplished by discretization (projection onto a finite dimensional subspace) followed by regularization. If the discrete problem has high dimension, though, typically ...

Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary to apply regularization ...

The efficiency and effectiveness of most optimization algorithms hinges on the numerical linear algebra algorithms that they utilize. Effective linear algebra is crucial to their success, and because of this, optimization ...

Abstract. We present a paraUel variant of the inexact Newton algorithm that uses the Krylov multisplitting algorithm (KMS) to compute the approxrmate Newton direction. The algorithm can be used for solving unconstrained ...

Restoration of images that have been blurred by the effects of a Gaussian blurring function is an ill-posed but well-studied problem. Any blur that is spatially invariant can be expressed as a convolution kernel in an ...

Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary to apply regularization ...

Some very effective but expensive image reconstruction algorithms cannot be applied to large images because of their cost. In this work, we first show how to apply such algorithms to subimages, giving improved reconstruction ...

Choosing the regularization parameter for an ill-posed problem is an art based on good heuristics and prior knowledge of the noise in the observations. In this work we propose choosing the parameter, without a priori ...

In this study, we describe the algebraic computations required to implement the stochastic finite element method for solving problems in which uncertainty is restricted to right hand side data coming from forcing ...