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Abstract

A classical way to construct a quadrature formula is to approximate the integral \(\int\limits_a^b {f\left( t \right)} \)dt by \(\int\limits_a^b {H\left( {,f;t} \right)dt} \) where H(x, f; t) is the Hermite interpolation polynomial for the function f based on a given system of nodes x = {(x1, v1),..., (xn, vn)} (i.e. x1,...,xn of multiplicities v1,...,vn, respectively). The error E(x; f) of this quadrature rule is expressed by the divided difference f[x,x] of f at the points x and x. We have
$$E\left( {;f} \right) = \int\limits_a^b {f\left[ {,x} \right]{{\left( {x - {x_1}} \right)}^{{v_1}}}...{{\left( {x - {x_n}} \right)}^{{v_n}}}dx} $$

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References

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Copyright information

© Springer Basel AG 1982

Authors and Affiliations

  • Borislav Bojanov

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