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Inverse Parameter Estimation using Hamilton-Jacobi Equations
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
2013 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesisAlternative title
Inversa parameteruppskattningar genom tillämpning av Hamilton-Jacobi ekvationer (Swedish)
Abstract [en]

Inthis degree project, a solution on a coarse grid is recovered by fitting apartial differential equation to a few known data points. The PDE to consideris the heat equation and the Dupire’s equation with their synthetic data,including synthetic data from the Black-Scholes formula. The approach to fit aPDE is by optimal control to derive discrete approximations to regularized Hamiltoncharacteristic equations to which discrete stepping schemes, and parameters forsmoothness, are examined. By non-parametric numerical implementation thedervied method is tested and then a few suggestions on possible improvementsare given

Abstract [sv]

 I detta examensarbete återskapas en lösning på ett glest rutnät genom att anpassa en partiell differentialekvation till några givna datapunkter. De partiella differentialekvationer med deras motsvarande syntetiska data som betraktas är värmeledningsekvationen och Dupires ekvation inklusive syntetiska data från Black-Scholes formel. Tillvägagångssättet att anpassa en PDE är att med hjälp av optimal styrning härleda diskreta approximationer på ett system av regulariserade Hamilton karakteristiska ekvationer till vilka olika diskreta stegmetoder och parametrar för släthet undersöks. Med en icke-parametrisk numerisk implementation prövas den härledda metoden och slutligen föreslås möjliga förbättringar till metoden.

Place, publisher, year, edition, pages
2013. , 138 p.
Series
TRITA-MAT-E, 2013:26
Keyword [en]
Hamilton-Jacobi equation. Optimal control. Euler method.
Keyword [sv]
Hamilton-Jacobi ekvationer. Optimal styrning. Eulers stegmetoder
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-123092OAI: oai:DiVA.org:kth-123092DiVA: diva2:624555
Subject / course
Numerical Analysis
Educational program
Master of Science in Engineering -Engineering Physics
Uppsok
Physics, Chemistry, Mathematics
Supervisors
Examiners
Available from: 2013-06-01 Created: 2013-06-01 Last updated: 2013-06-22Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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  • Other locale
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Output format
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