On a Statistical Model of Strand and Westwater for the Numerical Solution of a Fredholm Integral Equation of the First Kind

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Abstract
A statistical model is presented which is useful in the solution of a Fredholm integral equation of the first kind and equivalent to one proposed by Strand and Westwater. The model and the related problem presented here are familiar to statisticians from the study of regression analysis and are essentially, “(GLM): Find the best linear unbiased estimate of β given the observation y which satisfies y = Hβ + e, e distributed as N (0, Γ).” Here y, β c are vectors, H is an ( m + n ) × k matrix, and Γ is a certain ( m + n ) × ( m + n ) positive definite, known matrix. The main content of the paper is that (GLM) provides an equivalent way of considering the problem of Strand and Westwater and is to be preferred by virtue of the rich store of results available for the study of (GLM) and its intrinsic geometric nature.