Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
Chebyshev collocation spectral-radius growth is setup-specific conditioning context
Scope note
For the cited Chebyshev–Gauss–Lobatto second-derivative collocation matrix with the Dirichlet boundary rows treated as in the source, Shen and Tang report spectral-radius growth of order . This is a source-specific conditioning observation for that matrix and boundary treatment. It is not a stability estimate for every BVP discretization, a convergence theorem for the algorithm Boundary-eliminated Chebyshev collocation for a two-point Dirichlet BVP, or evidence about any continuum PDE regularity question. This carrier records the source's reported scope and does not claim to prove the spectral-radius asymptotic.
Depends on
Used by
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Dependency tree · two levels
7 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Jie Shen and Tao Tang, Spectral and High-Order Methods with Applications, Ch. 2 (standard reference, not scraped)