What does this research mean for the field?

The φ-function method enables the construction of an optimal quadrature formula for approximating Fourier integrals that minimizes error and is exact for the functions e^(σx) and e^(-σx). Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to construct an optimal quadrature formula for accurately calculating Fourier integrals using the φ-function method.

May 20, 2026Russian Mathematics

Construction of an Optimal Quadrature Formula for the Approximate Calculation of Fourier Integrals Using the φ-Function Method

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The aim is to construct an optimal quadrature formula for accurately calculating Fourier integrals using the φ-function method.
Constructed a quadrature formula using the φ-function method for Fourier integrals.
Estimated the error of the quadrature formula using the integral of the square of the φ function from Hilbert space.
Calculated coefficients of the optimal quadrature formula for specific functions.
The optimal quadrature formula provides exact results for functions e^(σx) and e^(-σx) with σ being a nonzero real parameter.
Error estimation is minimized by selecting an optimal φ function based on the square integral value.
Demonstrated significantly improved accuracy in the numerical integration of Fourier integrals.

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Implication

Randomized trial constructs an optimal quadrature formula for Fourier integrals, indicating enhanced accuracy in numerical calculations.

Cite This Study

Hayotov et al. (2026) studied this question.

synapsesocial.com/papers/6a0d4ec0f03e14405aa99e65 https://doi.org/10.3103/s1066369x26700076

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Construction of an Optimal Quadrature Formula for the Approximate Calculation of Fourier Integrals Using the φ-Function Method

Key Points

Discussion

Implication

Cite This Study

Construction of an Optimal Quadrature Formula for the Approximate Calculation of Fourier Integrals Using the φ-Function Method

Key Points

Discussion

Implication

Cite This Study