Kernel-splitting technique for enclosing the solution of Fredholm equations of the first kind (Q1869603)

The numerical solution of linear Fredholm integral equations of the first kind is inherently difficult. The paper derives a numerical method for such equations, by a series expansion of the kernel, which is splitted into a finite rank degenerate part and an infinite-dimensional, normwise small remainder. By enclosing the remainder term, the original problem is transformed into a degenerate set-valued problem. For this problem is derived a numerical method that provides a rigorous control of approximation and roundoff error. This central part requires much background theory and reasoning, which is provided. The method is illustrated briefly by three small examples.