6533b855fe1ef96bd12afcd1
RESEARCH PRODUCT
About the reliability, efficiency, and meaning of the error estimates of a LAOCOON3-type NMR analysis system
R Laatikainensubject
Work (thermodynamics)Spectrum (functional analysis)Line (geometry)General EngineeringApplied mathematicsMeasure (mathematics)QuantumEigenvalues and eigenvectorsConfidence intervalReliability (statistics)Mathematicsdescription
Abstract The statistical error estimates of a LAOCOON3-type system are tested. The analyzabilities of a spectrum and spectral parameters are described by a new measure. The variation in the uncertainties of the parameters can be explained by correlation coefficients. According to the calculations made, the error estimates are normally quite reliable if the accuracy of the observed spectrum is known. In some cases the Newton-Raphson type of iteration does not converge or the confidence limits of the parameters are enormous or both; an example is discussed. It seems clear that one cannot avoid differing uncertainties of the parameters by changing the method of analysis, or that one can avoid them only to a limited extent by using line intensities in the analysis; the inaccuracies are quantum mechanical properties. The program used in the calculations contains modifications useful in this kind of problem; the program is described briefly. The results obtained in this work may be useful in any eigenvalue problem.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1977-08-01 | Journal of Magnetic Resonance (1969) |