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A Fast and Well-Conditioned Spectral Method

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Conventional wisdom states that spectral methods have high accuracy, but lead to dense and ill-conditioned linear systems. In this talk we present a spectral method that constructs almost banded and well-conditioned matrices for the solution of linear ODES with variable coefficients. We prove stability of the method, and show that the constructed matrices have a bounded condition number. The resulting algorithm can efficiently and reliably solved for solutions that require as many as a million unknowns. This is joint work with Sheehan Olver.

This talk is part of the Cambridge Analysts' Knowledge Exchange (C.A.K.E.) series.

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