
Low rank approximation of positive semidefinite symmetric matrices using Gaussian elimination and volume sampling
Positive semidefinite matrices commonly occur as normal matrices of lea...
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Adaptive stratified sampling for nonsmooth problems
Science and engineering problems subject to uncertainty are frequently b...
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Randomization and reweighted ℓ_1minimization for Aoptimal design of linear inverse problems
We consider optimal design of PDEbased Bayesian linear inverse problems...
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A Sensitivity Matrix Based Methodology for Inverse Problem Formulation
We propose an algorithm to select parameter subset combinations that can...
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A Uniform Bound of the Operator Norm of Random Element Matrices and Operator Norm Minimizing Estimation
In this paper, we derive a uniform stochastic bound of the operator norm...
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Minimalnorm static feedbacks using dissipative Hamiltonian matrices
In this paper, we characterize the set of staticstate feedbacks that st...
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Algebraic error analysis for mixedprecision multigrid solvers
This paper establishes the first theoretical framework for analyzing the...
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Monte Carlo Estimators for the Schatten pnorm of Symmetric Positive Semidefinite Matrices
We present numerical methods for computing the Schatten pnorm of positive semidefinite matrices. Our motivation stems from uncertainty quantification and optimal experimental design for inverse problems, where the Schatten pnorm defines a design criterion known as the Poptimal criterion. Computing the Schatten pnorm of highdimensional matrices is computationally expensive. We propose a matrixfree method to estimate the Schatten pnorm using a Monte Carlo estimator and derive convergence results and error estimates for the estimator. To efficiently compute the Schatten pnorm for noninteger and large values of p, we use an estimator using a Chebyshev polynomial approximation and extend our convergence and error analysis to this setting as well. We demonstrate the performance of our proposed estimators on several test matrices and through an application to optimal experimental design of a model inverse problem.
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