On the paper 'inverse methods for analyzing aerosol spectrometer measurements: A critical review'

S. Lekhtmakher*, M. Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper several statements of Kandlikar and Ramachandran concerning the one-to-one correspondence between the spectrometric channels and aerosol size classes, overlaps of the kernels of integral equation, errors of the algebraic systems' solutions and some inversion algorithms are discussed. It is shown that expression A-1 e (A-linear algebraic system matrix, e-vector of the experimental errors) cannot be interpreted as the standard deviation of random errors and its adequate interpretation is given. The expressions for standard deviation of the system's solution are derived using the error propagation formula. It is indicated that known inequality for the errors of linear systems' solutions including condition number of matrix cond is not applicable to the random errors, and the new inequality is given. The approach of smooth continuous size distribution function concept is shown to meet with difficulties since its actual realization is discrete, stochastic and has only two values: 0 and 1.

Original languageEnglish
Pages (from-to)867-873
Number of pages7
JournalJournal of Aerosol Science
Volume31
Issue number7
DOIs
StatePublished - Jul 2000
Externally publishedYes

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