A new form of trigonometric orthogonality and Gaussian-type quadrature
TLDR
In this article, it was shown that for any S 2n+1-point Gauss interpolation formula, r = [ n/2] + 1, r−1 of the nodes must lie within the interval [a, b], and the remaining node (which may or may not be in [a and b]) must be real.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1976-12-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Trigonometric interpolation.read more
Citations
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Trigonometric orthogonal systems and quadrature formulae
TL;DR: It is proved that the so-called orthogonal trigonometric polynomials of semi-integer degree satisfy a five-term recurrence relation and a numerical method for constructing the corresponding quadratures of Gaussian type is presented.
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An extension of the theory of orthogonal polynomials and Gaussian quadrature to trigonometric and hyperbolic polynomials
TL;DR: A class of functions was introduced by P. E. Koch (Research Report No. 72, Institute of Informatics, University of Oslo, 1982) that includes algebraic, trigonometric, and hyperbolic polynomials as mentioned in this paper.
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Note on trigonometric divided differences
TL;DR: An alternative to Lyche's recently proposed scheme for trigonometric divided differences and a Newton-type interpolation formula, obtained through the development of an earlier suggestion of the writer, appears to be simpler, neater in format, more symmetrical and easier to compute as mentioned in this paper.
References
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Trigonometric Interpolation and Predictor‐Corrector Formulas for Numerical Integration
TL;DR: In this paper, a predictor-corrector formula for stepwise numerical integration of y = Φ(x, y, y) was derived for n 1/2-point osculatory interpolation.