Akademik Veri Yönetim Sistemi
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, ss.1-16, 2026 (Scopus)
In computational applications, measurements are often collected at uniformly distributed locations. In such cases, standard polynomial interpolation may exhibit divergence due to the Runge phenomenon, and the associated interpolation process is known to be severely ill-conditioned. A practical remedy is to select mock-Chebyshev points for polynomial interpolation from a dense set of equally spaced points, thereby reproducing the favorable stability properties of Chebyshev nodes. However, relatively few studies address the efficient computation of these nodes.
This study proposes a new version of the fast algorithm introduced by Ibrahimoglu (A fast algorithm for computing the mock-Chebyshev nodes, Journal of Computational and Applied Mathematics, 373 (2020), 112336). The proposed approach uses the floor function to compute the ratio of distances between consecutive Chebyshev–Lobatto interpolation points. The resulting algorithm is fast and stable, consistently generating node distributions that satisfy the mock-Chebyshev requirements with linear computational complexity O(n), while reducing the size of the corresponding satisfactory uniform grid. The study also establishes a theoretical lower bound on the minimum number of equispaced nodes required to meet the mock-Chebyshev conditions. Finally, a bivariate extension to mock-Padua points on[-1,1]²is presented and validated through numerical experiments.