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The mathematical research of William Parry FRS
In this article we survey the mathematical research of the late William (Bill) Parry, FRS
A Polynomial Spectral Calculus for Analysis of DG Spectral Element Methods
We introduce a polynomial spectral calculus that follows from the summation
by parts property of the Legendre-Gauss-Lobatto quadrature. We use the calculus
to simplify the analysis of two multidimensional discontinuous Galerkin
spectral element approximations
Covariance estimation using conjugate gradient for 3D classification in Cryo-EM
Classifying structural variability in noisy projections of biological
macromolecules is a central problem in Cryo-EM. In this work, we build on a
previous method for estimating the covariance matrix of the three-dimensional
structure present in the molecules being imaged. Our proposed method allows for
incorporation of contrast transfer function and non-uniform distribution of
viewing angles, making it more suitable for real-world data. We evaluate its
performance on a synthetic dataset and an experimental dataset obtained by
imaging a 70S ribosome complex
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