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...For industrial and applied mathematics siam society vol no pp june updating the inverse of a matrix william w hager abstract sherman morrison woodbury formulas relate after small rank perturbation to original history these fomulas is presented variousapplicationsto statistics networks structural analysis asymptotic optimization partial differential equations are discussed express in terms ofthe this paper surveys ofthese we examine some applications where helpful key words updates perturbations ams mos subjectclassifications f response gene golub s suggestion that an expo sitory be prepared concerning various focus on following result ifboth i va u invertible then uv uisoften called capacitance suppose n x m with columns v rows from identity y see provides formula it modified by corrections observe iu useful situations much smaller than structure nice so effort involved evaluating correction iva relative inverting general special case column vector row simplifies z ca luva c lu frequen...