A note on the evaluation of bounded \(L_ 2\)-functionals at B-splines and its application to singular integral equations (Q788483)

An algorithm computing recursively the values of \(\int g(t)v(t)dt\), where g is an \(L_ 2\)-function and v is a B-spline, is presented. For the functions \(g_ s(t)=\log | s-t|\) the starting values of the recursion formula can be computed analytically. The problem is related to the numerical solution of integral equations with a logarithmic singularity.