The stability of the Gauss-Chebyshev method for Cauchy singular integral equations (Q1097671)

It is shown that the infinity condition number for the Gauss-Chebyshev method of the complete Cauchy singular integral equation of the first kind is bounded above and below by the condition number of the dominant equation times a constant. The condition number of the dominant equation is asymptotically equal to \(c_ 0\cdot n\cdot \ln (n)\). This implies that the Gauss-Chebyshev method is stable for very large n's.