Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses
Samo za registrovane korisnike
2013
Autori
Rakić, TijanaStanimirović, Zorica
Denić, Aleksandar
Marić, Miroslav
Jančić-Stojanović, Biljana
Medenica, Mirjana
Članak u časopisu (Objavljena verzija)
Metapodaci
Prikaz svih podataka o dokumentuApstrakt
A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second-order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succe...eded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright
Ključne reči:
interpolation polynomial with divided differences / interpolation polynomial with finite differences / chromatographic response modeling / optimization / objective functions / liquid chromatographyIzvor:
Journal of Chemometrics, 2013, 27, 12, 466-474Izdavač:
- Wiley-Blackwell, Hoboken
Finansiranje / projekti:
- Modelovanje različitih hromatografskih sistema sa hemometrijskim pristupom u farmaceutskoj analizi (RS-172052)
DOI: 10.1002/cem.2559
ISSN: 0886-9383
WoS: 000327885200004
Scopus: 2-s2.0-84889658636
Institucija/grupa
PharmacyTY - JOUR AU - Rakić, Tijana AU - Stanimirović, Zorica AU - Denić, Aleksandar AU - Marić, Miroslav AU - Jančić-Stojanović, Biljana AU - Medenica, Mirjana PY - 2013 UR - https://farfar.pharmacy.bg.ac.rs/handle/123456789/1895 AB - A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second-order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright PB - Wiley-Blackwell, Hoboken T2 - Journal of Chemometrics T1 - Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses VL - 27 IS - 12 SP - 466 EP - 474 DO - 10.1002/cem.2559 ER -
@article{ author = "Rakić, Tijana and Stanimirović, Zorica and Denić, Aleksandar and Marić, Miroslav and Jančić-Stojanović, Biljana and Medenica, Mirjana", year = "2013", abstract = "A novel approach to mathematical modeling of chromatographic responses based on interpolation polynomials with divided differences and with finite differences is discussed. These interpolational techniques as well as traditionally applied second-order polynomial models obtained by least squares are compared. Interpolation techniques can be useful in situations where commonly used linear or quadratic models are not applicable: when the nature of dependence is complex or the investigated factor intervals are broad. The three analyzed modeling techniques are incorporated in a design of experiments methodology for systematic development and optimization of liquid chromatographic methods. The direct modeling of retention factors is carried out first, while the objective function for final quality measurement is calculated last. An interpolation polynomial with divided differences resulted in a high quality fit compared with the results obtained by the other two modeling approaches and succeeded in locating the desired optimum. It is shown that this modeling technique can be a useful alternative for modeling of chromatographic responses. Copyright", publisher = "Wiley-Blackwell, Hoboken", journal = "Journal of Chemometrics", title = "Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses", volume = "27", number = "12", pages = "466-474", doi = "10.1002/cem.2559" }
Rakić, T., Stanimirović, Z., Denić, A., Marić, M., Jančić-Stojanović, B.,& Medenica, M.. (2013). Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses. in Journal of Chemometrics Wiley-Blackwell, Hoboken., 27(12), 466-474. https://doi.org/10.1002/cem.2559
Rakić T, Stanimirović Z, Denić A, Marić M, Jančić-Stojanović B, Medenica M. Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses. in Journal of Chemometrics. 2013;27(12):466-474. doi:10.1002/cem.2559 .
Rakić, Tijana, Stanimirović, Zorica, Denić, Aleksandar, Marić, Miroslav, Jančić-Stojanović, Biljana, Medenica, Mirjana, "Comparison of interpolation polynomials with divided differences, interpolation polynomials with finite differences, and quadratic functions obtained by the least squares method in modeling of chromatographic responses" in Journal of Chemometrics, 27, no. 12 (2013):466-474, https://doi.org/10.1002/cem.2559 . .