Preconditioning rectangular spectral collocation

2015/10/01 by Kui Du, Du, Kui · 2 citations
Computer Science · Engineering · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Scattering and Analysis #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1510.00195

openalex publication_date 2015/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely ill-conditioned as the number of collocation points increases. By introducing suitable Birkhoff-type interpolation problems, we present pseudospectral integration preconditioning matrices for the ill-conditioned linear systems in RSC. The condition numbers of the preconditioned linear systems are independent of the number of collocation points. Numerical examples are given.

Cited by

• Preconditioning fractional spectral collocation
• On well-conditioned spectral collocation and spectral methods by the integral reformulation

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