References

General References

  1. H. Abdollahi, M. Maeder, R. Tauler: Calculation and meaning of feasible band boundaries in multivariate curve resolution of a two-component system. Anal. Chem. 2009, 81(6), 2115-2122.
  2. H. Abdollahi, R. Tauler: Uniqueness and rotation ambiguities in multivariate curve resolution methods. Chemom. Intell. Lab. Syst. 2011, 108(2), 100–111.
  3. O.S. Borgen, B.R. Kowalski: An extension of the multivariate component-resolution method to three components. Anal. Chim. Acta 1985, 174, 1-26.
  4. S. Beyramysoltan, R. Rajkó, H. Abdollahi: Investigation of the equality constraint effect on the reduction of the rotational ambiguity in three-component system using a novel grid search method. Anal. Chim. Acta 2013, 791(0), 25-35.
  5. S. Beyramysoltan, H. Abdollahi, R. Rajkó: Newer developments on self-modeling curve resolution implementing equality and unimodality constraints. Anal. Chim. Acta 2014, 827, 1-14.
  6. P. J. Gemperline: Computation of the range of feasible solutions in self-modeling curve resolution algorithms. Anal. Chem. 1999, 71(23), 5398-5404.
  7. A. Golshan, H. Abdollahi, M. Maeder: Resolution of rotational ambiguity for three-component systems. Anal. Chem. 2011, 83(3), 836-841.
  8. A. Golshan, M. Maeder, H. Abdollahi: Determination and visualization of rotational ambiguity in four-component systems. Anal. Chim. Acta 2013, 796, 20-26.
  9. K. Neymeyr, M. Sawall: On the set of solutions of the nonnegative matrix factorization problem. SIAM J. Matrix Anal. Appl. 39 (2018), 1049-1069, , see also onlinelibrary.wiley.com or (431 kB PDF file).
  10. R. Rajkó, K. István: Analytical solution for determining feasible regions of self-modeling curve resolution (SMCR) method based on computational geometry. J. Chemom. 2005, 19(8), 448-463.
  11. R. Rajkó: Natural duality in minimal constrained self modeling curve resolution. J. Chemom. 2006, 20(3-4), 164-169.
  12. M. Sawall, K. Neymeyr: On the area of feasible solutions and its reduction by the complementarity theorem. Anal. Chim. Acta 2014, 828, 17-26, see also sciencedirect.com or (869 KB PDF file). The four component data set is available for download.
  13. M. Sawall, N. Rahimdoust, C. Kubis, H. Schröder, D. Selent, D. Hess, H. Abdollahi, R. Franke, Börner A. and K. Neymeyr: Soft constraints for reducing the intrinsic rotational ambiguity of the area of feasible solutions. Chemom. Intell. Lab. Syst. 2015, 149, 140-150, see also sciencedirect.com or (4.7MB PDF file)
  14. R. Tauler: Calculation of maximum and minimum band boundaries of feasible solutions for species profiles obtained by multivariate curve resolution. J. Chemom. 2001, 15(8), 627-646.
  15. X. Zhang, R. Tauler: Measuring and comparing the resolution performance and the extent of rotation ambiguities of some bilinear modeling methods. Chemom. Intell. Lab. Syst. 2015 147, 47-57.

FACPACK References

  1. A. Jürß, M. Sawall, K. Neymeyr: On generalized Borgen plots for three-component systems. I: From convex to affine combinations and applications to spectral data. J. Chemom. 29 (2015), 420-433, see also onlinelibrary.wiley.com or 431 kB PDF file. The data set is available for download.
  2. A. Jürß, M. Sawall, K. Neymeyr: On generalized Borgen plots II: The line-moving algorithm and its numerical implementation. J. Chemom. 2016, 30(11), 636-650, see also onlinelibrary.wiley.com or (180 kB PDF file).
  3. M. Sawall, C. Kubis, D. Selent, A. Börner, K. Neymeyr: A fast polygon inflation algorithm to compute the area of feasible solutions for three-component systems. I: Concepts and applications. J. Chemom. 2013, 27(5), 106-116, see also onlinelibrary.wiley.com or 2.7 MB PDF file. The data set is available for download.
  4. M. Sawall, K. Neymeyr: A fast polygon inflation algorithm to compute the area of feasible solutions for three component systems. II: Theoretical foundation, inverse polygon inflation and FACPACK implementation. J. Chemom. 2014, 28(8), 633-644, see also onlinelibrary.wiley.com or 726 KB PDF file.
  5. M. Sawall, C. Kubis, E. Barsch, D. Selent, A. Börner, K. Neymeyr. Peak group analysis for the extraction of pure component spectra. J. Iran. Chem. Soc. 2016, 13(2), 191-205, see also link.springer.com or (695 kB PDF file).
  6. M. Sawall, A. Jürß, H. Schröder, K. Neymeyr: On the analysis and computation of the area of feasible solutions for two-, three- and four-component systems. Book contribution in volume 30 of Data Handling in Science and Technology, "Resolving spectral mixtures" edited by C. Ruckebusch, Chapter 5, Elsevier 2016, see also (9.7 MB PDF file). The following data sets are available for download: 3 components and 4 components.
  7. M. Sawall, K. Neymeyr: A ray casting method for the computation of the area of feasible solutions for multicomponent systems: Theory, applications and FACPACK-implementation. Anal. Chim. Acta 2017, 960:40-52, 2017, see also (748 kB PDF file). The four component data sets are available for download: 1 subset and 4 subsets.
  8. M. Sawall, A. Jürß, H. Schröder, K. Neymeyr. Simultaneous construction of dual Borgen plots. I: The case of noise-free data. J. Chemom. 2017, 31(12), e2954, see also onlinelibrary.wiley.com or (0.4 MB PDF file). The data set is available for download.
  9. M. Sawall, A. Moog, C. Kubis, H. Schröder, D. Selent, R. Franke, A. Brächer, A. Börner, K. Neymeyr. Simultaneous construction of dual Borgen plots. II: Algorithmic enhancement for applications to noisy spectral data. J. Chemom. 2018, 32(6), e3012, see also onlinelibrary.wiley.com or (1.4 MB PDF file).
  10. M. Sawall, H. Schröder, D. Meinhardt, K. Neymeyr. On the area of feasible solutions and its computation with FACPACK. Book contribution in Comprehensive Chemometrics, 2nd Edition, Elsevier, edited by R. Tauler 2019.
  11. T. Andersons, M. Sawall, K. Neymey. Analytical enclosure of the set of solutions of the three-species multivariate curve resolution problem. J. Math. Chem. 2022, 60, 1750-1780, see also link.springer.com.
  12. M. Sawall, C. Ruckebusch, M. Beese, R. Francke. A. Prudlik, K. Neymeyr. An active constraint approach to identify essential spectral information in noisy data. Anal. Chim. Acta 2022, 1233, 340448, (4.8 MB. PDF file). T. Andersons, M. Sawall, K. Neymey. Analytical enclosure of the set of solutions of the three-species multivariate curve resolution problem. J. Math. Chem. 2022, 60, 1750-1780, see also sciencedirect.com or (4.8 MB PDF file)