Embree, Mark2013-07-242013-07-242013-07-242013-07-242012-122013-07-24December 2Hergenroeder, AJ. "Moment Matching and Modal Truncation for Linear Systems." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71657">https://hdl.handle.net/1911/71657</a>.https://hdl.handle.net/1911/71657While moment matching can effectively reduce the dimension of a linear, time-invariant system, it can simultaneously fail to improve the stable time-step for the forward Euler scheme. In the context of a semi-discrete heat equation with spatially smooth forcing, the high frequency modes are virtually insignificant. Eliminating such modes dramatically improves the stable time-step without sacrificing output accuracy. This is accomplished by modal filtration, whose computational cost is relatively palatable when applied following an initial reduction stage by moment matching. A bound on the norm of the difference between the transfer functions of the moment-matched system and its modally-filtered counterpart yields an intelligent choice for the mode of truncation. The dual-stage algorithm disappoints in the context of highly nonnormal semi-discrete convection-diffusion equations. There, moment matching can be ineffective in dimension reduction, precluding a cost-effective modal filtering step.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Modal truncationModel reductionMoment matchingDual-stage dimension reductionLanczosArnoldiSmoothnessDiscrete smoothnessLaplacianHeat equationConvection-diffusionInitial boundary value problemFourier seriesCoefficient decaySemi-discreteExplicit integrationForward EulerLinear time-invariant systemsThesis2013-07-24123456789/ETD-2012-12-328