Abstract
An iterative method is proposed for the construction of Gaussian quadrature formulae that contain preassigned nodes. The method is locally convergent of order two. It can be implemented in a way that every iteration step involves a number of arithmetical operations that depends quadratically on the number of nodes, and it provides a posteriori error estimates. A comparison is made with known methods. Numerical examples show the suitability of the method for some of the possible applications.
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Ehrich, S. (1993). On the Construction of Gaussian Quadrature Formulae containing Preassigned Nodes. In: Brass, H., Hämmerlin, G. (eds) Numerical Integration IV. ISNM International Series of Numerical Mathematics, vol 112. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6338-4_6
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DOI: https://doi.org/10.1007/978-3-0348-6338-4_6
Publisher Name: Birkhäuser, Basel
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