A fluorescence decay fit converges with Levenberg-Marquardt to a minimum where the…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Computational Physics · Scientific programming for physicists

Scientific Computing for Physicists, Ch Minimisation with guarantees, with constraints and with randomness

Problem

A fluorescence decay fit converges with Levenberg-Marquardt to a minimum where the damping parameter has been driven to

\mu\approx 0

and

J^{\mathsf T}WJ = \begin{pmatrix}40 & 5\\ 5 & 20\end{pmatrix}

with the fitted parameters made dimensionless by scaling. At the minimum, the covariance matrix of the fitted parameters is the same as it would be from an ordinary least-squares fit started close to the answer,

\mathrm{Cov} = (J^{\mathsf T}WJ)^{-1}

. ((a)) Find

\mathrm{Cov}

. ((b)) State the standard uncertainty of each parameter.

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