A note on Peano constants of Gauss-Kronrod quadrature schemes

AbstractFor the error R2n + 1GK of the Gauss-Kronrod quadrature formula Q2n + 1GK, we prove the precise asymptotic value of the low-order Peano constants cs(R2n + 1GK), where s is fixed for increasing n. The result is applied for comparisons of the Gauss-Kronrod formula Q2n + 1GK with the Gauss formula QnG and with the Gauss formula Q2n + 1G, with respect to this often used quality measure