Tables of Alpert Quadrature Nodes and Weights




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  2nd-order Alpert Quadrature Rule for integrals of the form $\int_{0}^{1}f(x)+g(x)\log(x)\, dx$, with a = 1


    NODES                 & WEIGHTS                   \\

   1.591549430918953e-01  & 5.000000000000000e-01     \\



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6th-order Alpert Quadrature Rule for integrals of the form $\int_{0}^{1}f(x)+g(x)\log(x)\, dx$, with a = 3


     NODES                   & WEIGHTS                \\

     4.004884194926570e-03   & 1.671879691147102e-02  \\

     7.745655373336686e-02   & 1.636958371447360e-01  \\

     3.972849993523248e-01   & 4.981856569770637e-01  \\

     1.075673352915104e+00   & 8.372266245578912e+00  \\

     2.003796927111872e+00   & 9.841730844088381e+00  \\



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10th-order Alpert Quadrature Rule for integrals of the form $\int_{0}^{1}f(x)+g(x)\log(x)\, dx$, with a = 6


     NODES                  & WEIGHTS                 \\

    1.175089381227308e-03   & 4.560746882084207e-03   \\

    1.877034129831289e-02   & 3.810606322384757e-02   \\

    9.686468391426860e-02   & 1.293864997289512e-01   \\

    3.004818668002884e-01   & 2.884360381408835e-01   \\

    6.901331557173356e-01   & 4.958111914344961e-01   \\

    1.293695738083659e+00   & 7.077154600594529e-01   \\

    2.090187729798780e+00   & 8.741924365285083e-01   \\

    3.016719313149212e+00   & 9.661361986515218e-01   \\

    4.001369747872486e+00   & 9.957887866078700e-01   \\

    5.000025661793423e+00   & 9.998665787423845e-01   \\



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16th-order Alpert Quadrature Rule for integrals of the form $\int_{0}^{1}f(x)+g(x)\log(x)\, dx$, with a = 10


     NODES                 & WEIGHTS                   \\

    8.371529832014113e-04  &  3.190919086626234e-03    \\

    1.239382725542637e-02  &  2.423621380426338e-02    \\

    6.009290785739468e-02  &  7.740135521653088e-02    \\

    1.805991249601928e-01  &  1.704889420286369e-01    \\

    4.142832599028031e-01  &  3.029123478511309e-01    \\

    7.964747731112430e-01  &  4.652220834914617e-01    \\

    1.348993882467059e+00  &  6.401489637096768e-01    \\

    2.073471660264359e+00  &  8.051212946181061e-01    \\

    2.947904939031494e+00  &  9.362411945698647e-01    \\

    3.928129252248612e+00  &  1.014359775369075e+00    \\
 
    4.957203086563112e+00  &  1.035167721053657e+00    \\

    5.986360113977494e+00  &  1.020308624984610e+00    \\
 
    6.997957704791519e+00  &  1.004798397441514e+00    \\

    7.999888757524622e+00  &  1.000395017352309e+00    \\

    8.999998754306120e+00  &  1.000007149422537e+00    \\