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Full-Text Articles in Physical Sciences and Mathematics
Commuting Perturbations Of Operator Equations, Xue Xu, Jiu Ding
Commuting Perturbations Of Operator Equations, Xue Xu, Jiu Ding
Faculty Publications
Let X be a Banach space and let T: X →X be a bounded linear operator with closed range. We study a class of commuting perturbations of the corresponding operator equation, using the concept of the spectral radius of a bounded linear operator. Our results extend the classic perturbation theorem for invertible operators and its generalization for arbitrary operators under the commutability assumption.
Fitting Parameter Uncertainties In Least Squares Fitting, R. Steven Turley
Fitting Parameter Uncertainties In Least Squares Fitting, R. Steven Turley
Faculty Publications
This article review the theory and practice of computing uncertainties in the fit parameters in least squares fits. It shows how to estimate the uncertainties and gives some numerical examples in Julia of their use. Examples are given and validated for both linear and nonlinear fits.
Polynomial Fitting, R. Steven Turley
Polynomial Fitting, R. Steven Turley
Faculty Publications
This article reviews the theory and some good practice for fitting polynomials to data. I show by theory and example why fitting using a basis of orthogonal polynomials rather than monomials is desirable. I also show how to scale the independent variable for a more stable fit. I also demonstrate how to compute the uncertainty in the fit parameters. Finally, I discuss regression analysis: how to determine whether adding an additional term to the fit is justified.
Perturbation Results For Projecting A Point Onto A Linear Manifold, Jiu Ding
Perturbation Results For Projecting A Point Onto A Linear Manifold, Jiu Ding
Faculty Publications
Some new results will be presented on the perturbation analysis for the orthogonal projection of a point onto a linear manifold. The obtained perturbation upper bound is with respect to the distance from the perturbed solution to the unperturbed manifold.