Abstract
In the recent paper Notaris (Numer. Math., 142:129–147, 2019) it has been introduced a new and useful class of nonnegative measures for which the well-known Gauss–Kronrod quadrature formulae coincide with the generalized averaged Gaussian quadrature formulas. In such a case, the given generalized averaged Gaussian quadrature formulas are of the higher degree of precision, and can be numerically constructed by an effective and simple method; see Spalević (Math. Comp., 76:1483–1492, 2007). Moreover, as almost immediate consequence of our results from Spalević (Math. Comp.,76:1483–1492, 2007) and that theory, we prove the main statements in Notaris (Numer. Math.,142:129–147, 2019) in a different manner, by means of the Jacobi tridiagonal matrix approach.
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This work was supported in part by the Serbian Ministry of Education, Science and Technological Development (Research Project: “Methods of numerical and nonlinear analysis with applications” (#174002)).
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Spalević, M.M. A note on generalized averaged Gaussian formulas for a class of weight functions. Numer Algor 85, 977–993 (2020). https://doi.org/10.1007/s11075-019-00848-x
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DOI: https://doi.org/10.1007/s11075-019-00848-x