In:
Journal of the ACM, Association for Computing Machinery (ACM), Vol. 15, No. 1 ( 1968-01), p. 100-114
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.
Type of Medium:
Online Resource
ISSN:
0004-5411
,
1557-735X
DOI:
10.1145/321439.321445
Language:
English
Publisher:
Association for Computing Machinery (ACM)
Publication Date:
1968
detail.hit.zdb_id:
2006500-0
detail.hit.zdb_id:
6759-3
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