Semi-analytic conjugate gradient method applied to a simple inverse heat conduction problem

On the most simple 1-D heat equation, a simple identication problem of heatux on one side from temperature measurement on the other side is solved with a conjugate gradient method (CGM). What is new in this well known and academic problem is that theCGM can be developped explicitely. This means that the CGM is given with explicit formulae into an approximation space split between a polynomial part and an exponential part. A ltering property of the CGM is deduced. These results correct and deepen the work of previous authors