Approximation of Hilbert and Hadamard transforms on (0, +infinity)

作者：De Bonis Maria Carmela; Occorsio Donatella^*

来源：Applied Numerical Mathematics, 2017, 116: 184-194.

DOI：10.1016/j.apnum.2016.12.001

• Hypersingular integrals
• Hadamard finite part
• Lagrange interpolation
• Orthogonal polynomials
• Approximation by polynomials

The authors propose a numerical method for computing Hilbert and Hadamard transforms on (0, +infinity) by a simultaneous approximation process involving a suitable Lagrange polynomial of degree s and "truncated" Gaussian rule of order m, with s << m. The proposed procedure is convergent and pointwise error estimates are given. Finally, some numerical tests confirming the theoretical error estimates are presented.

• 出版日期2017-6