Taking both the hub and any spoke will count as an 18.3xx class for math majors, similar to 18.330, and as 16.90 for course-16 majors. Instructor: Prof. Steven G. Johnson. Lectures: MWF10 in 2-142 ...

We apply the well known Rayleigh–Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh–Ritz variational principle to ensemble states. By means ...

Abstract: The aim of this paper is to investigate a direct numerical method for solving a class of a fractional variational problem (FVP). The fractional derivative in the FVP is in the Caputo sense.

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We give a simple proof of the well known fact that the approximate eigenvalues provided by the Rayleigh-Ritz variational method are increasingly accurate upper bounds to the exact ones. To this end, ...

This paper considers the sparse generalized eigenvalue problem (SGEP), which aims to find the leading eigenvector with at most $k$ nonzero entries. SGEP naturally ...

ABSTRACT: When trying to fit data to functions of the eigensystem of a pde-eigenvalue problem, such as Maxwell’s equation, numerical differentiation is ineffective and analytic gradients must be ...

ABSTRACT: Partial differential equations arise in formulations of problems involving functions of several variables such as the propagation of sound or heat, electrostatics, electrodynamics, fluid ...