Accession Number : ADA256529


Title :   Iterative Algorithms for Integral Equations of the First Kind With Applications to Statistics


Descriptive Note : Technical rept.,


Corporate Author : HARVARD UNIV CAMBRIDGE MA DEPT OF STATISTICS


Personal Author(s) : Vangel, Mark


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a256529.pdf


Report Date : Oct 1992


Pagination or Media Count : 187


Abstract : This dissertation explores the use of a preconditioned Richardson iterative algorithm for the solution of linear and nonlinear ill-posed integral equations of the first kind. The discussion consists of three parts, which can be roughly categorized as: numerical analysis, applications to statistical methodology, and an application to an inverse problem. In the first part, singular matrix equations that result from discretizing ill-posed integral equations of the first kind are considered. Sufficient conditions for the convergence of Richardson's algorithm to a solution are established, and necessary and sufficient conditions are proven for special cases. The inconsistent case is also discussed. A preconditioning for equations with positive kernels leads to the Conditional Expectation algorithm, which is discussed in detail. A notion of 'iterative regularization' is introduced and related to the more usual penalized least squares approach to regularization.


Descriptors :   *ALGORITHMS , *INTEGRAL EQUATIONS , *ITERATIONS , METHODOLOGY , INTEGRALS , NUMERICAL ANALYSIS , APPROACH , STATISTICS , THESES , CONVERGENCE , EQUATIONS


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE