ISSN:
0886-9383
Keywords:
Multicomponent analysis
;
Iterative refinement
;
Simplex method
;
Condition numbers
;
Linear programming
;
Chemistry
;
Analytical Chemistry and Spectroscopy
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
Notes:
Concentration estimates of components present in a sample mixture can be obtained using matrix mathematics. In the past, the condition number of the calibration matrix has been used to give an amplification factor by which uncertainties in data can work through to errors in the concentration estimates. This paper explores an additional interpretation of condition numbers with regards to significant figures and rounding errors. A procedure is suggested which will always give the most accurate concentration estimates provided the calibration matrix is not too ill-conditioned. Condition numbers have also been used by analytical chemists to discuss the error bounds for concentration estimates. Unfortunately, only one representative error bound can be approximated for all the components. This paper will show how to compute bounds for individual concentration estimates obtained as solutions to a system of m equations and n unknowns. The procedure is appropriate when calibration data and sample responses are inaccurate.
Additional Material:
1 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/cem.1180030211
