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On numerical improvement of Gauss-Lobatto quadrature rules. (English) Zbl 1070.65019
Summary: It is well known that the Gauss-Lobatto quadrature rule \[ \int^1_{-1} f(x)\,dx\simeq \sum^n_{i=1} w_if(x_i)+ pf(-1)+ qf(1), \] is exact for polynomials of degree at most \(2n+ 1\). We are going to find a formula which is approximately exact for monomials \(x^j\), \(j= 0,1,\dots, 2n+ 3\) instead of being analytically exact for monomials \(x^j\), \(j= 0,1,\dots, 2n+ 1\). We also consider a class of functions for which the new formula produces better results.

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
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