Dec 26, 2023 · Title:On the best convergence rates of lightning plus polynomial approximations. Authors:Shuhuang Xiang, Shunfeng Yang, Yanghao Wu. View a PDF ...
Missing: xα. | Show results with:xα.
Apr 14, 2024 · Trefethen and his collaborators in [7] introduced a new lightning approximation with either a low-degree polynomial basis built on a new choice ...
Missing: xα. | Show results with:xα.
For σ > 2π/√α, the convergence rate is O(e-4π2(σ/√N)). The choice of σ = 2π/√α achieves the fastest convergence rate among all σ > 0, confirming the conjecture ...
Dec 26, 2023 · The new scheme achieves the optimal convergence rate for approximation of $x\alpha$ on $[0,1]$ as by the best rational approximation shown by ...
Missing: xα. | Show results with:xα.
The root-exponential convergence of lightning plus polynomial approximation ... On the best convergence rate of lightning plus polynomial approximation for xα.
실수 지수 함수 xα에 대한 번개 플러스 다항식 근사는 특정 매개변수 σ = 2π/√α를 사용할 때 최적의 수렴률을 달성할 수 있다.
polynomial approximations of xα on exponentially graded meshes on [0, 1]. We speak for simplicity in terms of mesh refinement by factors of 1/2, though the ...
The convergence rates in the maximum norm are of course rather poor since the functions are not analytic and thus the polynomial approximations converge slowly.
Missing: lightning plus
When using optimal parameters, the lightning approximation to xα matches the convergence rate of the best nonlinear rational approximation, as determined by ...
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A final advantage for this method is that it works directly on the Mathieu equation and the modified Mathieu equation both, so that both Mathieu functions and ...