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Mathematics > Numerical Analysis

arXiv:1803.09446 (math)
[Submitted on 26 Mar 2018 (v1), last revised 4 Nov 2019 (this version, v10)]

Title:Convergent kernel-based methods for parabolic equations

Authors:Yumiharu Nakano
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Abstract:We prove that the functions constructed by the kernel-based regressions with Wendland kernels under $\ell_1$-norm constraints converge to unique viscosity solutions of the corresponding fully nonlinear parabolic equations. A key ingredient in our proof is the max-min representations of the nonlinearities of the equations.
Subjects: Numerical Analysis (math.NA); Optimization and Control (math.OC)
Cite as: arXiv:1803.09446 [math.NA]
  (or arXiv:1803.09446v10 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1803.09446

Submission history

From: Yumiharu Nakano [view email]
[v1] Mon, 26 Mar 2018 07:31:35 UTC (84 KB)
[v2] Wed, 7 Nov 2018 06:00:34 UTC (109 KB)
[v3] Fri, 12 Apr 2019 02:37:26 UTC (82 KB)
[v4] Sat, 6 Jul 2019 05:00:42 UTC (1 KB) (withdrawn)
[v5] Thu, 18 Jul 2019 05:57:36 UTC (81 KB)
[v6] Wed, 24 Jul 2019 14:20:55 UTC (1 KB) (withdrawn)
[v7] Thu, 25 Jul 2019 02:20:03 UTC (1 KB) (withdrawn)
[v8] Fri, 26 Jul 2019 12:44:35 UTC (81 KB)
[v9] Wed, 30 Oct 2019 05:50:41 UTC (1 KB) (withdrawn)
[v10] Mon, 4 Nov 2019 13:59:36 UTC (80 KB)
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