Error Analysis for the Stereological Estimation of Sphere Size Distribution: Abel Type Integral Equation
Abstract
Computational errors are analyzed for existing schemes and their variants of estimating the sphere size distribution from the observed size distribution of cross sections. First, possible methods are classified according to their discrete approximation schemes of the basic integral equation, and the condition numbers of the coefficient matrices are examined. Then, asymptotic forms of error are derived. It is shown that the main source of error is the singularity of the basic integral equation of Abel type and that the magnitude of the error largely depends on the treatment of the singularity. Numerical examples are also given.
 Publication:

Journal of Computational Physics
 Pub Date:
 January 1985
 DOI:
 10.1016/00219991(85)900440
 Bibcode:
 1985JCoPh..57..229K