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Chebyshev Expansions for Solutions of Linear Differential Equations (0906.2888v1)
Published 16 Jun 2009 in cs.SC
Abstract: A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators. This interpretation lets us give a simple view of previous algorithms, analyze their complexity, and design a faster one for large orders.
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