Minimum-RMS Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind
Otto Neall Strand, E. R. Westwater · SIAM Journal on Numerical Analysis · 1968
An estimate of the quadrature approximation to the solution of an integral equation of the first kind is derived. This estimate has a minimum expected mean-square error among all linear unbiased estimates. Expressions for the resulting expected mean-square error are derived, and numerical comparisons are made with an earlier solution. A consistent theory of optimum representation of the solution in terms of basis vectors is derived; this theory is only approximated by the classical theory. The minimum possible mean-square error may be used as a quality criterion for the solution and is identical to the quality criterion of the earlier solution.