Two numerical approaches to the non-linear least-squares method via practical examples

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27230%2F18%3A10241110" target="_blank" >RIV/61989100:27230/18:10241110 - isvavai.cz</a>

Výsledek na webu

<a href="http://evlm.stuba.sk/APLIMAT2018/proceedings/" target="_blank" >http://evlm.stuba.sk/APLIMAT2018/proceedings/</a>

DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Two numerical approaches to the non-linear least-squares method via practical examples

Popis výsledku v původním jazyce

Our contribution is meant to be an example of multidisciplinary approach to the teaching of numerical methods. By employing the Michaelis-Menten&apos;s model for enzyme kinetics, we show a practical application of numerical methods in biochemistry. Given the experimental data, we find a dependence of a reaction rate on a concentration of a substrate. In a preliminary section, we derive and explain The Michaelis-Menten kinetics from behaviour of biochemical reactions. In a first part, the problem is linearized and then solved by the least squares method. In a second part, we do not use linearization and solve the original problem by the Newton&apos;s method for systems of non-linear equations. We conclude our contribution with a comparison of both approaches and results. We also offer several problems for students to clarify and deepen their understanding of the linearization. Our solution is provided in a form of a thoroughly commented Matlab Code.

Název v anglickém jazyce

Two numerical approaches to the non-linear least-squares method via practical examples

Popis výsledku anglicky

Our contribution is meant to be an example of multidisciplinary approach to the teaching of numerical methods. By employing the Michaelis-Menten&apos;s model for enzyme kinetics, we show a practical application of numerical methods in biochemistry. Given the experimental data, we find a dependence of a reaction rate on a concentration of a substrate. In a preliminary section, we derive and explain The Michaelis-Menten kinetics from behaviour of biochemical reactions. In a first part, the problem is linearized and then solved by the least squares method. In a second part, we do not use linearization and solve the original problem by the Newton&apos;s method for systems of non-linear equations. We conclude our contribution with a comparison of both approaches and results. We also offer several problems for students to clarify and deepen their understanding of the linearization. Our solution is provided in a form of a thoroughly commented Matlab Code.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

50302 - Education, special (to gifted persons, those with learning disabilities)

Projekt

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Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Aplimat 2018 : proceedings of the 17th conference on applied mathematics : February 6-8, 2018, Bratislava, Slovak Republic

ISBN

978-80-227-4765-3

ISSN

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e-ISSN

neuvedeno

Počet stran výsledku

9

Strana od-do

670-678

Název nakladatele

Slovak University of Technology

Místo vydání

Bratislava

Místo konání akce

Bratislava

Datum konání akce

6. 2. 2018

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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