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A new approach for constructing mock-Chebyshev grids
Yildiz Technical University

Corresponding Author:[email protected]

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Polynomial interpolation with equidistant nodes is notoriously unreliable due to the Runge phenomenon, and is also numerically ill-conditioned. By taking advantage of the optimality of the interpolation processes on Chebyshev nodes, one of the best strategies to defeat the Runge phenomenon is to use the mock-Chebyshev points, which are selected from a satisfactory uniform grid, for polynomial interpolation. Yet, little literature exists on the computation of these points. In this study, we investigate the properties of the mock-Chebyshev nodes and propose a subsetting method for constructing mock-Chebyshev grids. Moreover, we provide a precise formula for the cardinality of a satisfactory uniform grid. Some numerical experiments using the points obtained by the method are given to show the effectiveness of the proposed method and numerical results are also provided.
31 Dec 2020Submitted to Mathematical Methods in the Applied Sciences
05 Jan 2021Submission Checks Completed
05 Jan 2021Assigned to Editor
11 Jan 2021Reviewer(s) Assigned
16 Apr 2021Review(s) Completed, Editorial Evaluation Pending
21 Apr 2021Editorial Decision: Revise Minor
02 May 20211st Revision Received
02 May 2021Assigned to Editor
02 May 2021Submission Checks Completed
04 May 2021Reviewer(s) Assigned
05 May 2021Review(s) Completed, Editorial Evaluation Pending
18 May 2021Editorial Decision: Revise Minor
22 May 20212nd Revision Received
23 May 2021Submission Checks Completed
23 May 2021Assigned to Editor
25 May 2021Reviewer(s) Assigned
09 Jun 2021Review(s) Completed, Editorial Evaluation Pending
30 Jul 2021Editorial Decision: Accept
Dec 2021Published in Mathematical Methods in the Applied Sciences volume 44 issue 18 on pages 14766-14775. 10.1002/mma.7741