Regularised discretisations obtained from first‐kind Fredholm operator equations

Judicious discretisations of certain first‐kind Fredholm operator equations are tantamount to Fredholm infinite‐matrix equations of the second kind. We give detailed explanations for the occurrence of this interesting and useful phenomenon and carefully examine the behaviour of the discretisations, especially with respect to matrix condition numbers. Our main tool is a certain equivalence of the discretisations――within the context of finite matrices―to discretisations of Fredholm operator equations of the second kind.