TY - JOUR

T1 - On the paper 'inverse methods for analyzing aerosol spectrometer measurements

T2 - A critical review'

AU - Lekhtmakher, S.

AU - Shapiro, M.

N1 - Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2000/7

Y1 - 2000/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034010489&partnerID=8YFLogxK

U2 - 10.1016/S0021-8502(99)00561-3

DO - 10.1016/S0021-8502(99)00561-3

M3 - 文章

AN - SCOPUS:0034010489

VL - 31

SP - 867

EP - 873

JO - Journal of Aerosol Science

JF - Journal of Aerosol Science

SN - 0021-8502

IS - 7

ER -