Construction of Laguerre pseudospectral differentiation matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918461814341632 |
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| author | Nel, Emma Hale, Nicholas |
| author_facet | Nel, Emma Hale, Nicholas |
| contents | In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using an existing fast algorithm that also generates the collocation nodes. For the diagonal entries, a closed-form expression is employed to improve numerical accuracy. This construction avoids the catastrophic cancellation present in classical formulations and yields an all-in-one procedure for generating differentiation matrices. Numerical experiments demonstrate improved robustness and sustained high accuracy for significantly larger numbers of collocation points compared to standard implementations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20536 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Construction of Laguerre pseudospectral differentiation matrices Nel, Emma Hale, Nicholas Numerical Analysis 65L60 In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using an existing fast algorithm that also generates the collocation nodes. For the diagonal entries, a closed-form expression is employed to improve numerical accuracy. This construction avoids the catastrophic cancellation present in classical formulations and yields an all-in-one procedure for generating differentiation matrices. Numerical experiments demonstrate improved robustness and sustained high accuracy for significantly larger numbers of collocation points compared to standard implementations. |
| title | Construction of Laguerre pseudospectral differentiation matrices |
| topic | Numerical Analysis 65L60 |
| url | https://arxiv.org/abs/2604.20536 |