NDLI: Statistical Estimation of the Numerical Solution of a Fredholm Integral Equation of the First Kind

Content Provider	ACM Digital Library
Author	Strand, Otto Neall Westwater, Ed R.
Copyright Year	1968
Abstract	A method for the numerical solution of a Fredholm integral equation of the first kind is derived and illustrated. The method employs an a priori constraint vector together with covariances of both the constraint vector and the measurement errors. The method automatically incorporates an optimum amount of smoothing in the sense of maximum-likelihood estimation. The problem of obtaining optimum basis vectors is discussed. The trace of the covariance matrix of the error in the solution is used to estimate the accuracy of the results. This trace is used to derive a quality criterion for a set of measurements and a given set of constraint statistics. Examples are given in which the behavior of the solution as obtained from a specific integral equation is studied by the use of random input errors to simulate measurement errors and statistical sampling. The quality criterion and behavior of the trace of the error covariance matrix for various bases is also illustrated for the equation being considered.
Starting Page	100
Ending Page	114
Page Count	15
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/321439.321445
Journal	Journal of the ACM (JACM)
Volume Number	15
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1968-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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