## Computation of Gauss-Jacobi Quadrature Nodes and Weights with Arbitrary Precision

### Dariusz Brzeziński

DOI: http://dx.doi.org/10.15439/2018F107

Citation: Proceedings of the 2018 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 15, pages 297–306 (2018)

Abstract. In the paper there are presented efficient and accurate methods of Gauss-Jacobi nodes and weights computation. They include an enhancement for standard iteration method for Jacobi polynomials zeros finding, weight function formula transformation for increased accuracy of fractional derivatives computation and arbitrary precision application for mitigation of double precision arithmetic flaws. The results of numerical experiments presented in the paper prove high accuracy and efficiency of developed methods for computation of quadrature' nodes and weights, decreased amount of required iterations for polynomials zeros finding and elimination of truncation errors during weights computation. The application of arbitrary precision enables computing, which accuracy is limited only by accessible hardware.

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