Solution of integral equations using generalised inverse, function-valued Padé approximants, I

摘要

Neumann series solutions for the linear integral equation φ(x) = 1 + λ∫10{1 +⨍x − y⨍}φ(y) d y⨍⨍ converge for small values of λ. We use generalised inverse, function-valued Padé approximants to accelerate the convergence of the Neumann series and to estimate the singular value of λ. These estimates are found to compare very favourably with those from the Fredholm determinant method and the Padé approximant method.