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The Reduced Basis Method (RBM) is a model reduction technique used to solveparametric PDEs that relies upon a basis set of solutions to the PDE atspecific parameter values. To generate this reduced basis, the set of a smallnumber of parameter values must be strategically chosen. We apply a Metropolisalgorithm and a gradient algorithm to find the set of parameters and comparethem to the standard greedy algorithm most commonly used in the RBM. We testour methods by using the RBM to solve a simplified version of the governingpartial differential equation for hyperspectral diffuse optical tomography(hyDOT). The governing equation for hyDOT is an elliptic PDE parameterized bythe wavelength of the laser source. For this one-dimensional problem, we findthat both the Metropolis and gradient algorithms are potentially superioralternatives to the greedy algorithm in that they generate a reduced basiswhich produces solutions with a smaller relative error with respect tosolutions found using the finite element method and in less time.

Alternatives for Generating a Reduced Basis to Solve the Hyperspectral Diffuse Optical Tomography Model