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Convergence-Rate Deterioration of Spectral Differentiation for Singular Functions

A pointwise error analysis showing how spectral differentiation of Jacobi (and Chebyshev) polynomial approximations loses accuracy when the underlying function has an algebraic singularity: each extra order of differentiation costs two orders of convergence at the endpoints, one order in the smooth interior, and a parity-dependent or endpoint-dependent amount at the singularity itself, rigorously justifying the error-localization property of Jacobi approximation.

Zoe Graystone Text

On the deterioration of convergence rate of spectral diﬀerentiations for functions with

A numerical-analysis paper studying how the pointwise convergence rate of spectral differentiation degrades when the differentiated function contains singularities. Spectral differentiation (differen…