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"exponentially ill-posed"
Kind of a harsh-sounding term, don't you think? Context:
The authors consider an inverse heat conduction problem in a quarter
plane. The goal of the specific inverse problem is to determine the
surface heat flux in a body from a measured temperature history at a
fixed location inside the body. The standard example is the sideways
heat equation. This type of inverse problem is known to be
exponentially ill-posed.
Fortunately,
The authors propose a Fourier regularization method and prove order
optimal logarithmic stability estimates. A simple numerical example is
presented to verify the analytical results.
Phew!
ha ha ha
The authors consider an inverse heat conduction problem in a quarter
plane. The goal of the specific inverse problem is to determine the
surface heat flux in a body from a measured temperature history at a
fixed location inside the body. The standard example is the sideways
heat equation. This type of inverse problem is known to be
exponentially ill-posed.
Fortunately,
The authors propose a Fourier regularization method and prove order
optimal logarithmic stability estimates. A simple numerical example is
presented to verify the analytical results.
Phew!
ha ha ha