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Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 323--331 | DOI:10.5890/DNC.2024.06.010

C.R. Jisha, Ritesh Kumar Dubey$^{\dag}$

Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur-603203, Tamilnadu, India

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Abstract

One and two-parameter families of high-degree interpolating polynomials are constructed using the Lagrange polynomial, which is closest to a given ``nice" polynomial. The problem of finding such closest polynomial is formulated as an optimization problem using the area between polynomials. The explicitly computable optimizer is uniquely deduced. Numerical results are given for high order polynomial which is closest to target piecewise linear and piecewise cubic spline interpolations. These results demonstrate that despite of high degree, the optimized polynomial is less oscillatory and mimics the ``nice" non-oscillatory property of the target polynomial.

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