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The instrument spreading correction in GPC. III. The general shape function using singular value decomposition with a nonlinear calibration curve
Author(s) -
Rosen Edward M.,
Provder Theodore
Publication year - 1971
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1971.070150712
Subject(s) - singular value decomposition , mathematics , series (stratigraphy) , fourier series , nonlinear system , fourier transform , function (biology) , mathematical analysis , least squares function approximation , integral equation , calibration , algorithm , statistics , physics , paleontology , quantum mechanics , evolutionary biology , estimator , biology
The Gram‐Charlier series was suggested as an empirical instrument spreading function in the first paper (part I) of this series. In the second paper (part II) of this series, the Fourier transform method was used together with the suggested series to solve Tung's integral equation. In this paper, an alternate method for solving Tung's equation is proposed which eliminates some of the limitations of the Fourier transform method. In the approach used in this study, Tung's integral equation is approximated by a set of linear equations. Since no unique least‐squares solution can be computed, a closely related problem whose solution closely approximates the original problem is formulated and solved using singular value decomposition. By avoiding the use of the smallest singular values and forcing the equality of the areas of the corrected and the uncorrected chromatograms, an approximate solution to the original problem is obtained in which the oscillations inherently present due to the ill‐posed nature of the problem are filtered out. The performance of the method with the experimental data given in Part II is indicated.