An analog of the Sinc approximation for periodic functions
Hidenori Ogata
TL;DR
This paper introduces a new interpolation formula for periodic functions, analogous to the Sinc approximation, with proven exponential convergence for analytic cases, supported by theoretical analysis and numerical tests.
Contribution
The paper presents a novel interpolation formula for periodic functions that extends the Sinc approximation concept with proven exponential convergence.
Findings
The proposed formula converges exponentially for analytic periodic functions.
Theoretical error bounds are established for the interpolation method.
Numerical examples confirm the effectiveness of the new approximation.
Abstract
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval. Theoretical error analysis and numerical examples show that the proposed formula converges exponentially for analytic periodic functions.
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Taxonomy
TopicsIterative Methods for Nonlinear Equations · Mathematical functions and polynomials