Nonlinear least-squares fitting of multivariate absorption data

The introduction of fast scanning and diode-array spectrophotometers facilitates the acquisition of large series of absorption spectra as a function of reaction time (kinetics), elution time (chromatography), or added reagent (equilibrium investigations). It is important to develop appropriate programs that are able to handle the wealth of data and to extract all information. In this contribution a new application of factor analysis in a nonlinear least-squares fitting algorithm is presented

[1]  D. Marquardt An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[2]  J. Kankare Computation of equilibrium constants for multicomponent systems from spectrophotometric data , 1970 .

[3]  E. A. Sylvestre,et al.  Elimination of Linear Parameters in Nonlinear Regression , 1971 .

[4]  P. Gans Numerical methods for data- fitting problems , 1976 .

[5]  S. Wold Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

[6]  Joe M. Davis,et al.  Statistical theory of component overlap in multicomponent chromatograms , 1983 .

[7]  Jay R. Knutson,et al.  Simultaneous analysis of multiple fluorescence decay curves: A global approach , 1983 .

[8]  Avraham Lorber,et al.  Validation of hypothesis on a data matrix by target factor analysis , 1984 .

[9]  H. Gampp,et al.  Copper(II) complexes with linear pentadentate chelators , 1984 .

[10]  H. Gampp,et al.  Calculation of equilibrium constants from multiwavelength spectroscopic data-III Model-free analysis of spectrophotometric and ESR titrations. , 1985, Talanta.

[11]  H. Gampp,et al.  Calculation of equilibrium constants from multiwavelength spectroscopic data--II: SPECFIT: two user-friendly programs in basic and standard FORTRAN 77. , 1985, Talanta.

[12]  Ludwig Brand,et al.  Global and Target Analysis of Complex Decay Phenomena , 1985 .

[13]  H. Gampp,et al.  Calculation of equilibrium constants from multiwavelength spectroscopic data-I Mathematical considerations. , 1985, Talanta.

[14]  Paul J. Gemperline,et al.  Target transformation factor analysis with linear inequality constraints applied to spectroscopic-chromatographic data , 1986 .

[15]  Roland. Delley,et al.  Modifying the Gaussian peak shape with more than one time constant , 1986 .

[16]  H. Gampp,et al.  Calculation of equilibrium constants from multiwavelength spectroscopic data-IV Model-free least-squares refinement by use of evolving factor analysis. , 1986, Talanta.

[17]  Mees,et al.  Singular-value decomposition and embedding dimension. , 1987, Physical review. A, General physics.

[18]  Rigorous convergence algorithm for fitting a monoexponential function with a background term using the least-squares method. , 1987, Analytical chemistry.

[19]  J. Foley,et al.  Equations for chromatographic peak modeling and calculation of peak area , 1987 .

[20]  H. Gampp,et al.  Evolving Factor Analysis , 1987 .

[21]  M. Maeder Evolving factor analysis for the resolution of overlapping chromatographic peaks , 1987 .

[22]  Edmund R. Malinowski,et al.  Theory of the distribution of error eigenvalues resulting from principal component analysis with applications to spectroscopic data , 1987 .

[23]  Application of robust eigenvectors to the compression of infrared spectral libraries , 1988 .

[24]  K. Karlin,et al.  Kinetic and thermodynamic studies on the reaction of oxygen with two dinuclear copper(I) complexes , 1988 .

[25]  H. Kihara,et al.  Study of equilibria in 0.03 mM molybdate acidic aqueous solutions by factor analysis applied to ultraviolet spectra , 1988 .

[26]  E. R. Malinowski,et al.  Evolutionary Factor Analysis , 1988, Journal of Research of the National Bureau of Standards.

[27]  Marcel Maeder,et al.  Computerized data acquisition and data reduction in spectrophotometric analysis Part 2: numerical analysis with and without an underlying chemical model , 1988 .

[28]  Marcel Maeder,et al.  Evolving factor analysis, a new multivariate technique in chromatography , 1988 .

[29]  H. Gampp,et al.  Comment on rigorous convergence algorithm for fitting a monoexponential function with a background term using the least-squares method , 1988 .

[30]  Gerrit Kateman,et al.  Reliability of iterative target transformation factor analysis when using multiwavelength detection for peak tracking in liquid chromatographic separations , 1988 .

[31]  B. Kowalski,et al.  Numerical and statistical properties of target factor analysis methods , 1989 .

[32]  A. N. Papas Chromatographic Data Systems: A Critical Review , 1989 .

[33]  J. Grimalt,et al.  Resolution of overlapping peaks in gas and liquid chromatography , 1989 .

[34]  Temperature-dependent solute retention time variations, base-line drifts, and solute peak splits during the analysis of fenvalerate by a high-performance liquid chromatography/diode array system. , 1989, Analytical chemistry.

[35]  Edmund R. Malinowski,et al.  Statistical F‐tests for abstract factor analysis and target testing , 1989 .

[36]  Paul J. Gemperline,et al.  Conditions for detecting overlapped peaks with principal component analysis in hyphenated chromatographic methods , 1989 .